Division By Zero

[JarodRussell]

This thread feels like a division by zero.

I was just throwing out a number, guys. I didn't mean that infinity was actually the answer to this. My point, again, is that maybe 24th century understanding would have something more to say about division by zero.

Dude, this is just... seriously.

Basic math, dude.
1/1 = 1
1/0.5 = 2
1/0.25 = 4
1/0.125 = 8
1/0.001 = 1,000
1/0.0001 = 10,000
1/0.00001 = 100,000
The closer you get towards 0, the greater the result. Hence 1/0 = Infinity.

NOTHING WILL EVER CHANGE THIS.

And there will be no "greater understanding" in the future. This is seriously one of the worst examples you could have picked.

 

[Captain McBain]

This thread feels like a division by zero.

I was just throwing out a number, guys. I didn't mean that infinity was actually the answer to this. My point, again, is that maybe 24th century understanding would have something more to say about division by zero.

Dude, this is just... seriously.

Basic math, dude.
1/1 = 1
1/0.5 = 2
1/0.25 = 4
1/0.125 = 8
1/0.001 = 1,000
1/0.0001 = 10,000
1/0.00001 = 100,000
The closer you get towards 0, the greater the result. Hence 1/0 = Infinity.

NOTHING WILL EVER CHANGE THIS.

And there will be no "greater understanding" in the future. This is seriously one of the worst examples you could have picked.

Ok, seriously...

I guess that's why mathematicians say that 1/0 is undefined. They don't say it's equal to infinity. And how do you know that our understanding of the concept of zero won't change in the next several hundred years? We don't have the same understanding of infinity or other mathematical concepts that we had 10,000 years ago, so why is our understanding of zero automatically going to be the same?

 

[Captain McBain]

So what if humans can't really grasp infinity. Can Data grasp it, either? Or is it just a mathematical concept to him, the same as it is to me.

As for a sense of humor, since Soong seemed to have one, why wouldn't he give Data one? Lore seemed to have one.

Based on what we currently know of infinity, I doubt that even Data could fully grasp it. He is, after all, still a finite being. I think the only Star Trek being that could fully comprehend infinity is Q.

That was Soong's good pleasure. God didn't give all humans the ability to play the piano or build bridges; everyone has their own talents. Soong is Data's creator, and he was not obligated to design Data in any particular fashion.

 

[Pavonis]

Ok, seriously...

I guess that's why mathematicians say that 1/0 is undefined. They don't say it's equal to infinity. And how do you know that our understanding of the concept of zero won't change in the next several hundred years? We don't have the same understanding of infinity or other mathematical concepts that we had 10,000 years ago, so why is our understanding of zero automatically going to be the same?

Not everything in human knowledge is up for change in the future. Some things are just as well understood now as they're ever going to be. I think the concept of zero is one of those things. Sorry to burst your bubble.

 

[DonIago]

We might as well ask whether Data will have a greater understanding of the word "table"...

 

[xvicente]

Data squoze Tasha's jugs. Who cares about Math?

 

[Captain McBain]

Ok, seriously...

I guess that's why mathematicians say that 1/0 is undefined. They don't say it's equal to infinity. And how do you know that our understanding of the concept of zero won't change in the next several hundred years? We don't have the same understanding of infinity or other mathematical concepts that we had 10,000 years ago, so why is our understanding of zero automatically going to be the same?

Not everything in human knowledge is up for change in the future. Some things are just as well understood now as they're ever going to be. I think the concept of zero is one of those things. Sorry to burst your bubble.

You did not burst my bubble. I've already stated that our knowledge of zero may well be the same in the future. I never stated that we'd absolutely have new understanding of it.

 

[Zameaze]

I guess that's why mathematicians say that 1/0 is undefined. They don't say it's equal to infinity.

Division by zero is an "undefined operation" means it is impossible to have a real number answer to the equation. If you asked Data to divide by zero, his head wouldn't explode, he would just recognize the request as an impossibility, the same as if he were asked to count to Infinity, or to square a circle.

 

[Belz...]

No, I wasn't kidding.

Division by zero is impossible because there is no number that, multiplied by zero, leads to anything but zero.

I'm not math wiz but sense when does 49/0 = infinity?

No, because infinity times zero is still zero. You just can't divide by zero and get a number. That's why calculators give you Error as an answer and not infinity.

 

[JirinPanthosa]

If you asked Data to answer 49 / 0, he would probably explain the answer to the equation from the perspective of several different cultures and mathematical theories.

Some would say the answer is undefined because no matter how many times you multiply the number zero you can not reach any number other than zero. Contrarily, some would take limit points of zero into account and say the answer is Infinity. However...

He would go on like that for about two hours.

 

[Silvercrest]

You did not burst my bubble. I've already stated that our knowledge of zero may well be the same in the future. I never stated that we'd absolutely have new understanding of it.

Then the answer is: If our understanding of zero is the same, then dividing by zero will still be an undefined operation. Data would have the same understanding of it ... though as noted, he could go on for hours about it.

If our understanding of zero is different, then dividing by zero would also be defined differently. There's no way for us to predict what that means. In which case the answer regarding Data is, "Sure, why not?" At that point we're just making stuff up anyway.

And nothing says the understanding would be limited to Data or that he'd understand it any better. If there's somehow a different definition, then everyone might know it.

I guess that's why mathematicians say that 1/0 is undefined. They don't say it's equal to infinity.

Division by zero is an "undefined operation" means it is impossible to have a real number answer to the equation. If you asked Data to divide by zero, his head wouldn't explode, he would just recognize the request as an impossibility, the same as if he were asked to count to Infinity, or to square a circle.

True for most people. But if Kirk asked it, Data's head would explode.

 

[Reeborg]

No, I wasn't kidding.

I'm not math wiz but sense when does 49/0 = infinity?

No, because infinity times zero is still zero.

I doubt that. In fact: Infinity*Zero = undefined/not solvable but NOT Zero. Lim (X-> INF) X * (1/X) = INF * ZERO = ONE but Lim (X-> INF) (2*X) * (1/X) = INF * ZERO = TWO. Conclusion there is NO (exact) solution to Infinity*Zero; and most certainly it's not = ZERO.

 

[CorporalCaptain]

No, I wasn't kidding.

I'm not math wiz but sense when does 49/0 = infinity?

No, because infinity times zero is still zero.

I doubt that. In fact: Infinity*Zero = undefined/not solvable but NOT Zero. Lim (X-> INF) X * (1/X) = INF * ZERO = ONE but Lim (X-> INF) (2*X) * (1/X) = INF * ZERO = TWO. Conclusion there is NO (exact) solution to Infinity*Zero; and most certainly it's not = ZERO.

Actually, also, in your notation, Lim (X-> INF) X * exp(-X) = INF * ZERO = ZERO.

Proof, by l'Hôpital's rule: Lim (X-> INF) X * exp(-X) = Lim (X-> INF) X / exp(X) = Lim (X-> INF) 1 / exp(X) = Lim (X-> INF) exp(-X) = ZERO. QED.

INF * ZERO is one of the indeterminate forms.

 

[Gary7]

It's a rather glaring fault with Star Trek, the depiction of computers and sentient androids. No back-ups per se (you can't copy the EMH program's current data state in case of corruption?). And androids/computers that can be tricked when presented with unsolvable problems or mysterious conundrums.

When Norman broke down because of the "I'm a liar" and "He's lying" bit, I gritted my teeth. They COULDN'T be that stupid, right? RIGHT? Oh yeah... I forgot--this is one of those "comedy" episodes that you're not supposed to take seriously.

The only circumstance that was "sort of" plausible was Nomad. Its prime function was to sterilize imperfections and now it was shown how it was imperfect. Yet... it couldn't fathom "correction"? A mistake of identity is an error, but once corrected the error is in the past. The present state of the machine is "perfection" once again until successfully challenged later. Not to drag this thread off into a Nomad discussion, but I always felt it was such a loss for Nomad to be destroyed, and could have been prevented. Such as Kirk saying "Nomad, exercise priority override to shut down for critical repairs. Do not sterilize. You can be repaired."

 

[JarodRussell]

Your examples are from the friggin' 60s, where sophisticated computers were pretty much nothing more than a wet dream.

The EMH is a different beast. The idea behind it is sound, but the writers constantly confuse the hologram (which is just the visual representation, NOTHING more) and the actual program behind it.

That they can't create backups for the entire modified/evolved EMH is silly, but not that silly. If an AI grows really complex, it might be impossible to back it up as a whole, and recreate an identical version from those backups.

The EMH DID have an episode where his program went nuts because of a contradiction. But that was a complex moral problem that might be believable for a complex AI. It wasn't just a simple boolean logic problem.

 

[CorporalCaptain]

No, because infinity times zero is still zero.

I doubt that. In fact: Infinity*Zero = undefined/not solvable but NOT Zero. Lim (X-> INF) X * (1/X) = INF * ZERO = ONE but Lim (X-> INF) (2*X) * (1/X) = INF * ZERO = TWO. Conclusion there is NO (exact) solution to Infinity*Zero; and most certainly it's not = ZERO.

Actually, also, in your notation, Lim (X-> INF) X * exp(-X) = INF * ZERO = ZERO.

Proof, by l'Hôpital's rule: Lim (X-> INF) X * exp(-X) = Lim (X-> INF) X / exp(X) = Lim (X-> INF) 1 / exp(X) = Lim (X-> INF) exp(-X) = ZERO. QED.

INF * ZERO is one of the indeterminate forms.

Just to round things out, I should also point out that one can have, as it were, INF * ZERO = INF.

Spoiler: How

Construct an example from the one I used for INF * ZERO = ZERO, by reciprocation.

Lim (X-> INF) exp(X) * (1/X) = Lim (X-> INF) exp(X) / X = Lim (X-> INF) exp(X) = INF.

 

[Reeborg]

even INF * ZERO = INF^2

 

[GalaxyX]

This thread feels like a division by zero.

I was just throwing out a number, guys. I didn't mean that infinity was actually the answer to this. My point, again, is that maybe 24th century understanding would have something more to say about division by zero.

Dude, this is just... seriously.

Basic math, dude.
1/1 = 1
1/0.5 = 2
1/0.25 = 4
1/0.125 = 8
1/0.001 = 1,000
1/0.0001 = 10,000
1/0.00001 = 100,000
The closer you get towards 0, the greater the result. Hence 1/0 = Infinity.

NOTHING WILL EVER CHANGE THIS.

And there will be no "greater understanding" in the future. This is seriously one of the worst examples you could have picked.

I disagree with this.

The problem is that we have to define division into something as opposed to division into nothing

Thinking of it in the terms that you showed in your post is a logic flaw.

If you have 1 apple and you divide by 1, you're distributing that apple to 1 box.

If we divide the apple by 2 boxes, you have to cut it in half to put each half in it's separate box, hence the answer would be 0.5

Where it gets strange is when you divide by decimals.

If you divide 1 apple into 1/2 a box, the answer will be 2. Why? because the 1 box is split in half, and the answer 2, in this case, literally means "the 2 halves of the 1 apple". Mathematically 2 is correct, logically it's only correct because it's now considering that 1 apple to be logically "split" into the compartments of the same box.

So if you divide 1 apple by 0.1 boxes, the answer is 10.
Again, you're taking 1 box, and logically splitting it into 10 compartments. So when you stick that apple into 10 compartments in a box, the apple automatically gets logically split into 10 pieces that all make up the "1" apple.

And you can keep on doing that as much as you can go down in decimal spaces.


Now if you divide 1 apple into zero boxes, you are doing an illogical operation. There is NO box to divide the apple into. The zero itself, at least in this case is not a number, it's a symbol that represents the LACK of a number. There are zero boxes means exactly "there aren't any boxes at all"

So you cannot divide the apple into nothing, because there's nothing to divide the apple into. So the answer is "undefined" because it's illogical, like trying to put a circular peg into a square hole.

The answer is NOT infinity! The concept of dividing into smaller and smaller decimal #'s means, no matter how small, there is always "something" to divide into, no matter how small. As soon as you replace it with zero, you now have nothing to divide into, and you are trying to do an illogical operation.


I don't know if Data would explain it that way, but it's what makes most sense logically.