The Last Digit of Pi is Zero?

[LewisJ]

n = all the other digits of pi

n is not finite, n is impossible to define in this case

Um... you *did* define it right there.

By define I meant define explicitly, as in, writing the string out completely

 

[joey]

0 IS the last number of Pi.

 

[qqwref]

Hi there. This topic needs a good explanation of the Decimal Place Value System we know and love (but rarely look into deeply!). Having a not-quite-full understanding of this is where questions such as this topic's and the 0.9~ thing come from.

First off, the place value system does not define the number itself, but just represents it. It's an extremely convenient way to represent a number because you can get as close as you want with only a finite number of digits (and more digits = you can get closer). So that's pretty cool.
Second, the place value system basically constructs numbers by adding x + y/10 + z/100 + ..., where all the variables are integers. Anyway, as I've said we can get arbitrarily close to representing every number, but we can't exactly represent the number unless it can be written as some integer divided by some power of 10. So the important thing here is that if we put enough digits, we can get infinitely close to the number we want - and thus represent the number itself, for all intents and purposes.
Third, the real numbers as we normally define them do not contain any infinitely small intervals. What I mean is, if you take any two really close real numbers and subtract them, the number you will get is going to be close to 0 but only finitely close - unless it's 0, it will be at least as large as 1/x for some large enough integer x. This is a consequence of the definition of real numbers, which I'm not going to get into. Point is, this is pretty important because it means that if we define a number that is infinitely close to some other number (less than 1/x apart for every positive integer x), they are the same.

So what's this mean for our pi problem? Suppose you write out all the digits of pi (yes, ALL of them, infinitely many) and then stick a 0 at the end. Does that even mean anything? Not really, because remember that the place value system only has places for finitely numbered digits. There is no "infiniteth digit" because 1/(10^infinity) would be an infinitely small number and therefore equal to 0 (meaningless) in the real number system. So the place value system simply won't allow you to write a 0 'after' all the digits of pi because you can never get to the end anyway. After all, if you ever did reach the end it would mean that the digits of pi stop - that you can represent pi with some finite number of digits. But then pi would be a rational number (a fraction made out of integers), and it's actually been proven that that isn't the case. So talking about putting a 0 after all the digits of pi, or even about what the 'last digit' is, makes no sense at all. These concepts only exist in terms of the place value system, and the place value system only defines things in terms of finite numbers. Beyond that, any questions are meaningless.

 

[koreancuber]

Should I make a poll?

 

[DaijoCube]

There are literally an infinite number of solutions to any given scramble of a rubik's cube

Are there, excluding using stuff like (R R')x y?

Sure. Scramble a cube, then turn it however the hell you please for however long you please and then start solving it. That was a solution to the scramble.

Daijo, us being made of matter does not make everything predictable to the point that you can say what the last solve of a rubik's cube ever will be. I'm not even going to bother arguing this one with you, anyone who has had HS physics knows how ridiculous your claim is.

There is not a time where the sum of all forces won't be equal to the mass times the acceleration. I want to argue on this, but you must let your judgment aside. I'm in pure sciences and I love maths and physics over all other classes. I'm not saying that because I don't know anything.

Newton's second law has nothing to do with time (other than that a = d/dt v), which is in theory infinite, and thus, we do not know when the last solve of a rubik's cube will occur. In a less theory-based thought process, consider this: If I pick up a rubik's cube - completely ignoring the time issue - what calculations, simulations, or analyses can you do to predict the entire move sequence I will use to solve it?

I can't, nobody can. I said it was POSSIBLE. Not humanly possible though.

Human race necessary has an end (because the sun has an end), therefore we ''could'' know when the last Rubik would be solve.

 

[miniGOINGS]

qq, what 0.9~ thing?

 

[Stefan]

Pi in base pi is 1.0, so it's indeed 0, case closed. Or it's 1, your choice.

 

[miniGOINGS]

Pi in base pi is 1.0, so it's indeed 0, case closed.

I've never thought about using a different base (other than dec I mean). That seems like a legit answer though.

 

[Muesli]

There are literally an infinite number of solutions to any given scramble of a rubik's cube

Are there, excluding using stuff like (R R')x y?

Sure. Scramble a cube, then turn it however the hell you please for however long you please and then start solving it. That was a solution to the scramble.

Daijo, us being made of matter does not make everything predictable to the point that you can say what the last solve of a rubik's cube ever will be. I'm not even going to bother arguing this one with you, anyone who has had HS physics knows how ridiculous your claim is.

There is not a time where the sum of all forces won't be equal to the mass times the acceleration. I want to argue on this, but you must let your judgment aside. I'm in pure sciences and I love maths and physics over all other classes. I'm not saying that because I don't know anything.

Newton's second law has nothing to do with time (other than that a = d/dt v), which is in theory infinite, and thus, we do not know when the last solve of a rubik's cube will occur. In a less theory-based thought process, consider this: If I pick up a rubik's cube - completely ignoring the time issue - what calculations, simulations, or analyses can you do to predict the entire move sequence I will use to solve it?

I can't, nobody can. I said it was POSSIBLE. Not humanly possible though.

Human race necessary has an end (because the sun has an end), therefore we ''could'' know when the last Rubik would be solve.

When the sun goes pop what's to say we haven't colonised other planets?

 

[Stefan]

qq, what 0.9~ thing?

That 0.9999999..... = 1.

 

[DaijoCube]

It is, and it's quite cool

 

[DaijoCube]

There are literally an infinite number of solutions to any given scramble of a rubik's cube

Are there, excluding using stuff like (R R')x y?

Sure. Scramble a cube, then turn it however the hell you please for however long you please and then start solving it. That was a solution to the scramble.

Daijo, us being made of matter does not make everything predictable to the point that you can say what the last solve of a rubik's cube ever will be. I'm not even going to bother arguing this one with you, anyone who has had HS physics knows how ridiculous your claim is.

There is not a time where the sum of all forces won't be equal to the mass times the acceleration. I want to argue on this, but you must let your judgment aside. I'm in pure sciences and I love maths and physics over all other classes. I'm not saying that because I don't know anything.

Newton's second law has nothing to do with time (other than that a = d/dt v), which is in theory infinite, and thus, we do not know when the last solve of a rubik's cube will occur. In a less theory-based thought process, consider this: If I pick up a rubik's cube - completely ignoring the time issue - what calculations, simulations, or analyses can you do to predict the entire move sequence I will use to solve it?

I can't, nobody can. I said it was POSSIBLE. Not humanly possible though.

Human race necessary has an end (because the sun has an end), therefore we ''could'' know when the last Rubik would be solve.

When the sun goes pop what's to say we haven't colonised other planets?

Let me reformulate. If human race was to be extincted, it would be possible to know what would be the sequence of the last solve of a rubik cube.

 

[CubesOfTheWorld]

My opinion

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Pi goes on forever, so it does not actually end with any particular number.

 

[Chapuunka]

And the problem I see with this is that even if there were a last digit, and you added a zero onto it, you could easily keep adding on zeroes into a new infinity using the same logic.

 

[Mastersonian]

And the problem I see with this is that even if there were a last digit, and you added a zero onto it, you could easily keep adding on zeroes into a new infinity using the same logic.

*caugh* Sig Figs *caugh*

 

[daniel0731ex]

this thread got knocked up so quickly.

 

[TioMario]

There isn't such thing as the last digit of PI in the first place.
It's an irrational number, what means it has INFINITE numbers after the comma.

For more information: http://en.wikipedia.org/wiki/Real_number#Completeness

 

[Deleted member 4527]

Pi in base pi is 1.0, so it's indeed 0, case closed. Or it's 1, your choice.

LOL win proof.

It is possible to use irrational bases right?

 

[Diniz]

Pi in base pi is 1.0, so it's indeed 0, case closed. Or it's 1, your choice.

LOL win proof.

It is possible to use irrational bases right?

The only problem of irrational bases is that the representation may be not unique.

 

[Escher]

Well, I might create a philosophical debate here. At a specific moment in time, if we could know the position, speed, acceleration, mass and nature of all particle in the Universe, it would be MATHEMATICALLY possible to calculate every single event in the past and future.

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