QB64.org Forum
Active Forums => QB64 Discussion => Topic started by: Dimster on November 10, 2021, 10:32:30 am
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So, as we all know, math isn't my strongest suit. Wondering if I could get your thoughts on if there may be a math formula to do something with division by zero. In my case I have multiple calculation which produce for me a trending value. In the calculations I often come to the point where there is zero trending (ie where the divisor is zero). Now the direction of the trend is also being followed and once the divisor gets to zero, in my routines negative trending is allowed. Therefore I have struggled with trying to determine if "0" is positive or negative and I'm using the trending to make that determination. So a falling trend at zero, the formula needs to product a negative value, whereas a trend that has been rising suddenly hits a zero, I want that same math formula to produce a positive value. That sounds so convoluted but I hope you can grasp the idea.
Anyway. I have never been able to find a math formula to do what I have just described, so I have forced values. Here is an idea of what I mean by forced the value
a = 25
b = 0
c = a / b
a = 25
b = 0
c = a / b
If b
= 0 Then c
= -.001 ' value forced for a falling trend, would be +.001 for rising trend
By plugging a forced value I think I'm introducing some inaccuracies to my outputted values. Maybe there is a positive or negative number that I could use that is just 1 short of inf?
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What is the thing that might be 0 that also may be used as a divisor?
Most people would program:
if b <> 0 then c = a/b else 'handle the case when b is 0. eg, c = a or c = 0 usually depends on what b is.
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It seems a little strange and a little unfair when you think about it... You can 'add' zero to anything as well as 'subtract' and even 'multiply', but not 'divide'? Oh well. 3 out of 4 ain't bad... lol
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I agree with you @johnno56 . The value "0" is clearly a void which should mean "no number either positive or negative". A division by zero should be the same value as the numerator. 25/0 = 25 seems to make sense to me. How it becomes INF suggests we are trying to divide by an infinite number of values. I realize there is an apparent identical value if the divisor is 1 ie 25/1 = 25, which on the surface seems to be the same but there is a difference. If we accept that a division by zero is the same thing as just a repeat of the numerator, whereas a division by 1 is the actual number of times the divisor went into the numerator. This becomes evident for example if the equation is -25/-1 is positive 25 whereas -25/0 is a negative 25. Very difficult to work with a result of INF.
Thanks you guys for your input. I think I'm going to trap for a division by zero and then see what happens if I use a division by zero to mean its a repeat of the immediate previous result.
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If I didn't like INF, I'd give division by 0 the max number per data type.
If data_type is byte, a / 0 = SGN(A) * 127. (127 or -127)
If data_type is integer, a / 0 = SGN(A) * 32767 (32867 or -32767)
And on for other data types...
If I was graphing the points on a map, this would show an extreme blip off into infinity.
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@Dimster
Therefore I have struggled with trying to determine if "0" is positive or negative and I'm using the trending to make that determination. So a falling trend at zero, the formula needs to product a negative value, whereas a trend that has been rising suddenly hits a zero, I want that same math formula to produce a positive value. That sounds so convoluted but I hope you can grasp the idea.
To calculate the trend - whether it is declining or rising. Please try to specify. Namely, if you have, say, 1000 values, then you get a different trend for the whole range and a different trend for comparing, for example, the last 100 values. What you want to compare it with is also important. Is the default value for trend determination the maximum value from the set of all compared elements for a given period, or is it related to some specific value? I'll give an example.
Let's say you have 900 values from 900 to zero and then another hundred values from zero to hundred. If you want to determine a trend for all thousand numbers, the maximum is 1000 and 999 other values are less than a thousand, so this is a declining trend.
What happens if you compare only the last hundred values? The last hundred values are from zero to a hundred, as we agreed at the beginning of this example. Then it can be said that this is a growing trend, because in the last values 99 values are lower than the last value.
If we add another 100 values of the same size to these 100 values and we make a trend from these 100 values, we will find that the 100 values are just the same size and it is stagnation. That's how I look at it.
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Hi @Petr.. My trending is more a movement towards and away from Zero. Away from zero being positive and toward zero being negative. If there are more than 1 negative movements then a negative trend is forming, whereas more than 1 positive is a positive trend forming. So my conundrum is how to interpret zero. The math formula I'm using comes up with INF as a result when the data is hitting zero in the trending values.
Ideally I should take a INF result as meaning perfect balance and therefore no sign ( ie + or -) can be applied to the resultant of the math formula but the reality is that the events being monitor all have potential to occur. Because they have potential they can never have a perfect zero value therefore I'm trying to decide if "0" is a positive number or negative. I guess it would be similar to that situation where you walk towards a wall but only take 1/2 the distance of the previous step. You theoretically can never reach the wall but always have potential to do so.
Or Petr how do you decide if a variable is in a negative group or a positive group ( is x <= O the negative group or x < 0 the negative group, while x =>0 the positive group, or x > 0 is the positive group). Seems you have to decide here if O is positive or negative.
In my situation, I have been plugging in a positive value as close to zero as I dared. If the math calculated to INF then I used .000001 as the denominator. In effect conceding that I put zero in the positive group. But thinking more on what trending could mean and what INF could mean in terms of my trending, I'm looking more at it as a stall or a repeat in the trend. I'm going to go with capturing the last math result and just use it again every time the math comes up with INF result.
Boy I didn't mean to go on this long with my reply. Way too much thinking in coding.
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Alright let me shake this thread up. Who can calculate the value of:
sin(x) / x
at x=0.
I see a handful of different answers coming from this thread, but only one is correct. If you ponder this example enough, you may feel empowered to try division by zero in other contexts.
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ok, weird stuff coming:
division by 0
first off, zero has NO multiplicative inverse (https://en.wikipedia.org/wiki/Multiplicative_inverse). which is why a CPU would fail it.
Another interesting division fact, is that dividing by smaller and smaller numbers gives you bigger and bigger answers
Example:
10/2 = 5
10/1 = 10
10/.5 = 20
10/.4 = 25
etc...
as the divisor(?) reaches zero - the answers head toward infinity
so you would think that 10 / 0 = ∞
multiplicative rule:
0 x ∞ = 1
so
(0 x ∞) + (0 x ∞) = 2
this reduces down to
(0 x ∞) = 2
But this should = 1, sounds like that stupid school math LOL
so mathematically: 1 = 2 would be correct, if you can prove the above (but not in the real world)
found some more info on this
https://en.wikipedia.org/wiki/Riemann_sphere
how to make division by 0 work. LOL
enjoy
hmmmm
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But consider this Example as well:
-10/2 = -5
-10/1 = -10
-10/.5 = -20
-10/.4 = -25
etc...
as the divisor(?) reaches zero - the answers head toward -infinity
so you would think that -10 / 0 = -∞
Now move 10, -10 closer and closer together and you get -infinitiy adjacent to positive infinity at 0, so I think mathematicians have it right who say division by 0 is undefined.
So that' why I say in real world for practical questions you have to consider the thing you are dividing by and define the situation for what works for your case.
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So how does the infinite universe of negative numbers fit into all of this? If zero is both positive and negative at the same time then, theoretically we can have an equation:
+0 / -0
which would then give you a multiplicative inverse of -0 / +0
All math formulas result in either a positive or negative number. Infinity should be able to be grouped as negative infinity and positive infinity, which therefore should lead to a negative zero and a positive zero. Zero should be banned from the infinite universe as it is not a number. It can not take on a + or - sign and therefore should not exist.
On the other hand it should be treated as a negative value because it has negative connotations to it ... he's a zero .... you have zero money in your bank account .... you have lost zero weight in your diet ... etc, etc...
@STxAxTIC .. the answer is + NAN
@xra7en ... interesting stuff ( a lot over my head ) thanks for it all.
@bplus ... I like how you came up with negative infinity. I'm thinking infinity itself implies all conceivable numbers which would include negative numbers but if we lobby for the separation then at the very least a division by zero in qb64 should at least result in a -INF or +INF. Would help me a lot in my trending decisions.
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Alright so...
Stuff like
0 x ∞ = 1
so
(0 x ∞) + (0 x ∞) = 2
this reduces down to
(0 x ∞) = 2
But this should = 1, sounds like that stupid school math LOL
is something that I hope every curious person writes down at least once in their life... But it's super wrong.
As for the positive/negative infinity example you guys are fleshing out, I think it's summed up in a picture shamelessly screenshotted from my notes:
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The take-away here is you always need to specify from which direction you are approaching a limit. From the left, you get one answer, from the right, you get another answer. And that's all there is to say about that.
As for the sin(x) / x problem, I accidentally said the answer above. It's "one":
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What's the real real take-away here? An ounce of mathematics is better than 4 tons of code!
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@STxAxTIC - I did not read your notes on this issue before starting this thread, sorry about that.
If i'm following the examples correctly, there is a difference between "sin" and "sinc". It is the "sinc" formula which is giving the distinct negative/positive infinities. It appears sinc is the plugging in of a forced value "x". And this is exactly how I had been treating my INF results. I would just force a value for the denominator. But I was still having a worry that I needed to know if the plugged value should be + or - . Does "sinc" have a different outcome if x is negative? Would the charts be the same however just changing from the lower left/upper right quadrants to upper left/lower right?
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Lim(x->0) sin(x)/x
Bill (STxAxTIC) naturally gives us the mathematician's answer & proof. An engineer does it with a spreadsheet:
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Dimster - Seems like you want to be searching wikipedia for "even vs. odd functions" (they can do better with pictures than I can with words)... but lemme be honest: this is a total rabbit hole unless you're trying to step into calculus. Otherwise, I think the ready-fire-aim technique that works so brilliantly for shooting potatoes around the farm should get you by. (That is, just code and re-code until you get the behavior you want and explanations be damned.)
Qwerkey - When in doubt, use brute force! Nice number crunching there! I see the bottom results give what's expected.
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Anyone (looking at you qwerkey, prolly bplus too) want another challenge?
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See that? y = (n^x - 1) / x
What is the value of y at x=0?
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@STxAxTIC
Lim(x->0) (n^x - 1) / x
As any number to the power 0 is 1, I assumed that the answer is always 0 (it is if n=1). As you imagine that 'raising to the power' goes 'more quickly' than division, I assumed that the numerator get closer to zero than does the divisor. But spreadsheet shows this not to be the case.
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Thinking cap required.
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Division by zero is undefined. You simply can't do it. It's impossible to take *something* and divide it up to the point that *nothing* remains. Vice versa, it's also impossible to take an infinite number of *nothings* and have them turn into a number of *somethings*.
What STx keeps forgetting to mention is he's talking about THE LIMIT of his equations. For practical purposes, we can say SIN(0) / 0 = 1, but that's the same as SINGLE presion math -- it's just rounding after a certain number of arbitrary digits (infinity, in this case). I understand the concept -- as a farmer, I've used it all my life. "It's 3.2 miles from my house to the spring box where I get my water." And, it is.. Give or take a few miles depending on how much you get lost and meander around in the forest and mountains getting there. It's close enough for practical purposes, but it's not the mathematical answer of 3.1786437231475 miles, which is what GPS data gives as a mathematical response.
Practically, sin(0) / 0 = 1.
Mathematically, *anything*divided by zero is *undefined*.
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@STxAxTIC
I note that log(10) = 2.302585. So by inspection my answer is
log(n)
(For any critical reader, we are, of course, talking natural logs).
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Say, excellent analysis Qwerkey! The answer is indeed the natural log of n. That's a pretty keen eye you must have in order to just pluck that pattern out of a sea of numbers.
And I knew Steve would eventually take his shot. Homie, me and you been having this argument for the better part of a decade, on one forum or another, one thread or another, mostly calculated by me, admittedly. I try to "sneak" notions of calculus into.... just everything, all the time... and there you are, on each thread, reminding me that you still personally need to catch up to the 16th century in terms of mathematical reasoning. I forgive the Greeks for tripping themselves up in Zeno's paradox, not understanding concepts like convergence, etc., but that was thousands of years ago. Now... there's no possible way that you would take this lesson publicly, and only on a cold day in hell would you take this lesson publicly *from me*... so I'll leave that right there. Last word is yours if you want it but you gotta understand I needed to respond to what you said publicly and why its so important that you read a book on precalculus and retain what's in there!
Last time: I shouldn't even need to say this a second time because the proof is already in this thread, but sin(0)/0 is exactly 1, not approximately, not in the limit, but exact. The mechanic of this goes far deeper than booting up qb64.exe and trying PRINT Sin(0) / 0 to verify your bias. To claim this is all somehow the same a single precision math is ... just what? Don't confuse the tool with the wood itself.
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Moving on, regardless...
Qwerkey - for academic completeness, here is how I know its the natural log:
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Say, want another? This one is less about division by zero and closer to *multiplication* by zero, ooooh boy. Anyway, the formula is:
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So what you do is pick a number N, set up a loop that calculates all those square roots (with N total square roots taken). Then, multiply that result by 2^N and you might be shocked by the final answer.
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Last time: I shouldn't even need to say this a second time because the proof is already in this thread, but sin(0)/0 is exactly 1, not approximately, not in the limit, but exact. The mechanic of this goes far deeper than booting up qb64.exe and trying PRINT Sin(0) / 0 to verify your bias. To claim this is all somehow the same a single precision math is ... just what? Don't confuse the tool with the wood itself.
Okay, let's follow this irrefutable logic...
sin(0) / 0 = 1
Now, everyone knows that sin(0) = 0, so what you're *really* saying is that 0/0 = 1.
Now the following has to also be true, if we multiply both sides by 2:
2 * (sin(0)) / 0) = 2 * (1)
(2 * sin(0)) /( 2 * 0) = 2
2 * sin(0) / 0 = 2
Which sounds logical, until we realize that once again, sin(0) = 0, so what we have here is now:
2 * 0 / 0 = 2
0 / 0 = 2
But Stx just told us that sin(0) / 0 = 1! He irrefutably argued that 0 / 0 = 1! And yet, 0/0 is now both 1 and 2?!! (And any other number that we want to repeat this process with...)
sin(0) = 0, so the heart of his argument is that 0 / 0 = 1... But, we just proved that it was equal to 2?? GASP!!
And when it comes to the heart of the matter, WHAT IS DIVISION? Nothing but glorified subtraction, just as multiplication is glorified addition.
3 * 5 is the same as saying (add 3 to itself 5 times)... 3 * 5 = 3 + 3 + 3 + 3 + 3. Total is 15.
15 divided by 3 is the same as saying (how many times can I take 3 away from 15, before I hit 0?)... 15 / 3 = 15 - 3 - 3 - 3 - 3 - 3. Count those 3's and you end up with 5. 15 / 3 = 5.
Now, the problem comes when we ask about any number divided by 0.
How many times can you take nothing away from something, before reaching 0?
3 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 - 0 .... an infinite number of times, but we still have 3...
BUT, STx likes to argue that if you have nothing, you can take nothing from it exactly once, and still have nothing!! 0 - 0 = 0... The problem here is that you can *also* do this for infinity. 0 - (0 - 0 - 0) = 0. Well, I just subtracted 0 three times there and got 0 for the end result, so the answer has to be THREE! 0 / 0 = 3!!
You just can't do it. Division by zero is undefined -- just as much in the 61st century as it ever was back in the 16th.
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And for Qwerky, who likes charts, let's build one:
sin(x)/ x = ??? (The chart before seemed to indicate that it equaled 1.)
Let's simply multiply both sides by two... What is (2 * sin(x)) / (2 * x)??
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Just as before, our answer approaches 1...
So, (2 * sin(0)) / (2 * 0) = 1, according to the chart and the limit above.
Factor that 2 back out and we get: 2 (sin(0) / 0) = 1
And OBVIOUSLY, as STx has assured us above, (sin(0) / 0) = 1, so let's substitute that value in there.
2 * 1 = 1
And now we have irrefutable proof that 2 = 1!
Sounds about right to me. :P
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For a mathematician, Lim(x->0) sin(x)/x is definitely 1, so Bill is right, of course.
sin(x)/x is a 'special case' (?), as sin(x) -> x for small x (and increasingly accurate as x -> 0): the sin function is 1:1 linear near the origin. So the condition becomes 0/0 which is undefined, so Steve is right, of course.
Numbers! What a mystery the universe is.
How do mathematicians ever get to sleep with all that stuff going on?
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Bless your heart Qwerkey, trying to divide the cake evenly at the end. Unfortunately this issue is not a matter of democracy, or seeing things both ways, or honoring the length of one's filibuster post. (Could you say it shorter next time Steve? haha) There is really just one right approach to this:
For those still following, remember the definition of sinc = sin x / x in the first place. Looky here:
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The factor of "1/x" completely cancels out of the equation. I circled it for y'all. That is, I wish I could do that *clap* emoji... The *clap* sinc function *clap* contains *clap* no *clap* singular *clap* points!!!! Division by zero never occurs, at all.
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For a mathematician, Lim(x->0) sin(x)/x is definitely 1, so Bill is right, of course.
sin(x)/x is a 'special case' (?), as sin(x) -> x for small x (and increasingly accurate as x -> 0): the sin function is 1:1 linear near the origin. So the condition becomes 0/0 which is undefined, so Steve is right, of course.
Numbers! What a mystery the universe is.
How do mathematicians ever get to sleep with all that stuff going on?
The LIMIT is 1, but it's never actually one. It'll get infinitely close to 1, but never quite achieve that point. For *practical* purposes, you can often say it's one. For pure mathematical definition, it's indefinite/undefined, and for the reason I showed you above.
Ask Siri sometime what 0 dived by zero is. She'll set the issue straight.
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Bless your heart Qwerkey, trying to divide the cake evenly
Oh well, I tried.
Looks like it'll come to blows. Two pugilists in the ring, 15 rounds. Possibly shorter if one of the combatants ends up flat out on the canvass.
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Naaaah, I assured Steve he had the last word on the actual topic on hand (as far as he and i go), but I did break protocol once and repeat myself: my posts after that have been salvaging the public face of of this now-cringeworthy thread. I hope that nobody searching google for "qb64 division by zero" pulls up THIS thread, ya feel? Let's hope this just goes away and the take-away is you now know a cool formula for the natural log, can't deny that!
EDIT: BTW, There is still one more open puzzle on this page ^. Give that a stab (and see if we can't trigger steve all over again for breaking the rules in a new way)
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In formula sin(x) / x because sin() function is for angles. x has to be assumed an angle and angle 0 is equivalent to 2I*pi, I being some Integer.
So as I said before, pay attention to the thing you are dividing by because pure numbers don't have to take that into account.
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Interesting thought bplus, the trig functions do some nice work with angles, but it is not an axiomatic requirement that the argument in sin() be an angle. The argument can be any real number, any complex number - even an entire matrix, believe it or not - all inside the argument of sin(). (And no, putting sin() around a matrix does not simply mean you compute the sine of each component, that would be too easy, haha.)
The whole reason I brought up sin(x)/x in the first place is because it has a removeable singularity, which means it has no singularity. Honestly, between me and everyone, at this point I feel like nothing more than a troll for evoking the monty python-esque rebuttals to calculus that I knew were gonna come.
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EDIT: BTW, There is still one more open puzzle on this page ^.
Will try & have a go tomorrow.
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Brilliant minds, fabulous explanations
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@STxAxTIC
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Wow! So the bit after the negative sign never gets above 2 (the sum approaches 4). Another numbers marvel. So the quantity under the final square root approaches zero. Meanwhile the 2^n is increasing rapidly. From the number of nines in the quantity 1.999999.... and the number of places in the 2^n, as calculated by QB64, I deduce that the square root 'approaches zero quicker than the 2^n increases' (sorry for the mathematical gobbledegook): the answer is zero as n-> infinity.
Well, it's either zero or infinity.
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The whole reason I brought up sin(x)/x in the first place is because it has a removeable singularity, which means it has no singularity.
Another example to demonstrate this is take any function say f(x) = x^5+456*x
then define another function g(x) = f(x)*(x - 1)/(x - 1)
now g(x) demands a division by zero at x = 1 -- but you have done nothing to the function, you can cancel out the (x - 1) terms
g(x) = f(x) still holds
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Good morning boys
So Qwerkey! I can tell you're close. Did you try setting variable types as double? This piece of code captures the problem:
... And when you run that... Amazingly somehow*, you get the digits of pi! Good ole 3.14159... And in the case that N goes to infinity, the answer converges to exactly pi. Weird right? Infinity times zero equals pi? Damn right it is, if you pick your infinity properly and your zero properly.
* = (proof of all this on request)
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Vince, glad you piped into this conversation. You're damn right too: if you can factor a zero out of the denominator and cancel it with something upstairs, the singularity is gone.
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Photographic evidence
notice how an actual singularity looks in images f(z) = 1/z and f(z) = (z+1)/(z-1), the magnitude contours get closer and closer together as the function tends to infinity
then in image sinc(z) directly computed by dividing complex sine of z by z. Just as one might understand a function as "a rule to apply to a number" rather then "a set of pairs" with each pair rightfully justified. Notice how there's no evidence of a tendency to infinity at z = 0
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Vince with the one-two punch! What a cool plotting utility you've got there. Real textbook-quality crispness and coloring. Thanks for gracing this thread with those visuals - I've never pictured sinc(z) before.
For anyone who doesn't know why these are 2D plots, Vince is showing us the complex plane, not just the number line. (Activates tomato shield.) Everything we were discussing in this thread previously takes place on a thin horizontal line running through the middle of Vince's last plot.
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So Qwerkey! I can tell you're close.
Close? Nowhere near. I used double and then Float. Looks like I can't write code properly. Will try to get it right (having donned the class dunce cap).
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Good morning boys
So Qwerkey! I can tell you're close. Did you try setting variable types as double? This piece of code captures the problem:
... And when you run that... Amazingly somehow*, you get the digits of pi! Good ole 3.14159... And in the case that N goes to infinity, the answer converges to exactly pi. Weird right? Infinity times zero equals pi? Damn right it is, if you pick your infinity properly and your zero properly.
empirical tests suggest that the optimum value for n to give the most digits of Pi is n=ceiling((sqr(2)-1)*2*float_precision), for double the optimum n is 14
and the approximate digits of Pi is float_precision/2
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Yeah thats prolly true jack. This example would need high-precision libraries to really shine.
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Having corrected a slight coding error, I now see the proper result. Using Double (or Float) variable, the result switches from pi to zero at n > 25 (multiplication calculation error in number of nines in 1.9999....).
What is it saying about the universe that you can get pi (to do with circles) from square root of 2 (nothing to do with circles)???
Amazing.
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I must say, I absolutely love the conversation between Steve and Bill here. They are both talking over each other, but what exactly is the essence of the miscommunication?
Perhaps it's the limitation of notation, "sin(x)/x". If you are stuck in "arithmetic land", there's clearly a number on top and a number on the bottom. When the number on the bottom is zero, you simply can't do it. But is there a deeper way of looking at "sin(x)/x" other than a list of instructions to key into a calculator? That might be called limits, calculus, analysis, etc but there is no way to have that conversation within the limited language of "arithmetic land" and so it is impossible. Steve makes an attempt, "I get what you're saying it is sooo close it's practically..." but communication is not facilitated because they are speaking over each other in two different languages.
It reminds me of the age old "0.999..." -- is it sooo close it's practically one or is it just a misleading side effect of decimal notation? There is the concept of an infinite sum, 9/10 + 9/100 + 9/1000 + ..., which may converge or diverge but is 0.999... is an infinite sum, or does it just really looks like one? I guess it depends what "land" you are stuck in.
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Your are onto something there @_vince ... "It depends what land you are stuck in. I kinda like the remark made by @johnno56. You can do all but divide with zero. And I feel he has a point. Why if 1/1 =1, 2/2 = 1, 3/3 =1 can't 0/0 =1 ????? I can hear the guys groaning after all the proof they have just gone through. I'm thinking I'm going to do my own math with zero. I will give signs, like +0 or -0 and see if, especially in terms of trending, the results are logical and actionable.
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Compromise: lets redefine sinc to the pictured definition. Plug in x=0, the exponential e^0 evaluates to 1, and the integral becomes a 2x1 rectangle -- find its area, multiply by half ... = 1.
The integral itself is easy enough to solve being an exponential, it's simply exp(-i*x*t)/(-i*x) -- and, again, there's that dreaded x in the denominator! but if you plug in x=0, anything but the above answer is clearly wrong
This definition also gives a hint as to why sinc is so useful in engineering and whatnot (Fourier integrals, etc)
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Say, I like that definition vince!
It's really a shame that the people who *need* to see this kind of thing have long-since exited this thread on their tractors. True to form, he pipes up with the usual cringeworthy stuff during the "teacher trolls the students" phase, and then feeling victorious, does slow-motion donuts toward the door and out of the room.
Ever heard of "steel-manning?" That's where, if two sides disagree on something, and instead of straw-manning, the new polite thing to do is to summarize your opponent's position so perfectly well, that it pays a compliment to the view; does it good justice. In other words, make a solid case *for* your opponent's view, to the point where they say "couldn't have said it better myself". Once both sides agree this has been done, the conversation can move on to the actual "debate" part. Each side has to knock over the steel man of the other if they are to win.
My actual feeling is that Steve and I don't talk past each other. What everyone gets to read instead, and what seems to confuse a few others, is that I'm not really talking *to* Steve when I reply. There is an implicit "ladies and gentlemen, as you can see..." kind of thing behind my responses.
Anyway, back to the subject on hand:
Is there a derivative-based definition to compliment the integral definition? hmmm
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Geeez. I've tried to follow along using the internet to help me understand the math arguments you guys are making but the tread is heading way, way above me. And I gather it would be too difficult to dummy down the math, I would need to know a lot more just to understand a "dummy down" version anyway. So I'm going to bow out at this point and very much appreciate everyone's input on division by zero.
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Geeez. I've tried to follow along using the internet to help me understand the math arguments you guys are making but the tread is heading way, way above me. And I gather it would be too difficult to dummy down the math, I would need to know a lot more just to understand a "dummy down" version anyway. So I'm going to bow out at this point and very much appreciate everyone's input on division by zero.
It's simple Dimster: you *can't* divide by zero. Zero is one of those special existences which folks who should know better, like to pretend is just the same as any other number. They come up with "rules" which work, as long as you whistle idiotically and only apply them in specific situations like:
"Zero raised to *any* power is zero. " They'll draw you pretty pictures to prove their point...
Then, next week, they'll tell you: "Any number raised to the zero power is one." They'll draw more pictures to try and prove their point...
And then you have to ask, "What about zero raised to the zero power?" It can't exist under both definitions, unless you believe that 0 = 1... These instances are singular irregularities which they never bother to point out, just so they can go around quoting their favorite mantras and pretending they're smarter than you.
Truth is -- Zero is an irregularity simply because it represents NOTHING. Division by zero is simple to understand: Take one of anything and divide it into zero parts. If you can do that, you just destroyed the Law of Conservation. You turned *something* into *nothing*, much like STx does every time he bothers to open his mouth. 😝
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Btw, Dimster, this isn't really about dividing by zero it's about the sinc function.
Lecturing a physicist on the law of conservation? He won't be so merry-cherry!
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Yes finding another way to write sinc function without dividing by 0 was fine way to avoid div by 0 error.
You aren't going to convince QB64 you can divide by zero so find another way before you try.
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You are right that QB64 will not directly evaluate sin(0)/0, just as it will not evaluate sqrt(-144), just as it will not evaluate an integral. That's all up to the man behind the keyboard and what he is trying to do, only then can one recommend the optimal algorithm for the solution. And such abstract mathematical concepts do not cease to exist just because one is programming QB64.
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LOL did he really start with the zero-exponents thing?
0^0 = 1. Cry hard.
The question was never really "who is right?" anyway. The question has always been "who needs to be right?" If you don't absolutely need to be correct about concepts of calculus in order for your day-to-day programs, inventions, and christmas tree sales to come out properly... then you won't. To take it away from math for a second, I don't need to know Swahili in order to do my daily activities and obey traffic laws, and I would never in my wildest dreams actually double-down and argue over Swahili against a person who makes their living doing it.
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seems like we have been there before, 0^0 I mean
just out of curiosity I tried that expression in pari/gp, Maple, Mathematica, Maxima and C
C, pari/gp and Maple gave 1 as the answer
Mathematica gave Indeterminate
Maxima gave expt: undefined: 0^0
I vote for Mathematica and Maxima, although for practical purposes I would use 1 as the answer
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Don't mean to beat a beaten dead horse, but here's another interesting definition
https://www.wolframalpha.com/input/?i=simplify+1%2F%28gamma%28z%2Fpi+%2B+1%29*gamma%281+-+z%2Fpi%29%29 (https://www.wolframalpha.com/input/?i=simplify+1%2F%28gamma%28z%2Fpi+%2B+1%29*gamma%281+-+z%2Fpi%29%29)
which works out nicely:
sinc(0) = 1/(Gamma(1)Gamma(1)) = 1/(0! * 0!) = 1
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Another way to get Div by 0 error is trying to take Mod 0.
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Mr. _vince, I think something is not right, sin(0)=0 and the link that you gave does not agree with your png