Infinity

Anatoly · 2018-01-17 16:43:19

Bimps wrote:

peace wrote:
also take the number PI it has so much decimals
how many

Pi is irrational. That should explain everything.

Gosha · 2018-01-17 17:10:30

AnatolyEE wrote:

Pi is irrational

Pi equals to 4, are yo drunk?

Emma333 · 2018-01-17 17:53:17

u dummies the word pie stands for 1 pie, if it was more it would be pies!

LukeM · 2018-01-17 18:55:15

However 1 pie is equal to 2 pi :O

Edit: Staying on topic: Does this mean we can have infinite pie?

Emma333 · 2018-01-17 20:59:58

LukeM wrote:

However 1 pie is equal to 2 pi :O
https://image.prntscr.com/image/43_AvH6 … rU9MHQ.png
Edit: Staying on topic: Does this mean we can have infinite pie?

if you keep eating half of what's left of the pie you have infinite pie

HeyNK · 2018-01-18 00:02:26

actually that limit approaches 2

Ratburntro44 · 2018-01-18 00:41:35

LukeM wrote:

I wouldn't say it's a particularly formal proof, but I would still call it a proof (if not then where's the assumption or error?)
Edit: Also infinitesimal numbers are a thing and they =/= 0 (by definition), I think AnatolyEEs problem was that there isn't a very good numerical representation (don't think you can write them as 0.00...001) although I think his point explanation would be correct

it relies on the fact that 10*0.999... = 9.999..., which isn't clearly true without an actual definition of how decimals work. once could conceivably have a system in which 10*0.999... = 9.999...990; you need to actually strictly define how the representations of numbers work in order to do anything meaningful here

once you do have the definition (in summary, that the decimal string itself shows an infinite series, and the represented value is its sum), then you can go further. however, the proof presented still doesn't really work; infinite series can't necessarily be freely manipulated like that. however, it happens that all the series represented by decimal strings do converge

since 0.999... shows the series , which obviously converges to 1, it by definition represents the number 1

yes, infinitesimals exist (in some systems). no, it still doesn't work like he said. you can always get a smaller infinitesimal, so there's still no "next" number in any meaningful sense. one could conceivably define a system where infinitesimals come as integer multiples of a basic infinitesimal, but it would end up being pretty unintuitive and probably pointless. you are correct about 0.00...001

LukeM · 2018-01-18 01:43:38

I agree with your first paragraph, but as x.y - 0.y is clearly x, I don't see why you would need to worry about infinite series for the subtraction part

And (IIRC) infinitesimals are defined as a number smaller than any 1/n, but larger than 0, so surely the 'next' number after zero would be an example of one? (as it wouldn't matter that 'next' doesnt make sense for rational/real numbers as the definition states it isn't rational/real)

Ratburntro44 · 2018-01-18 02:05:28

in general, you can't manipulate infinite series in any way you might want. because of the nature of the series represented in decimals, it turns out that these are correct, but ends up being beside the point since dealing with the series directly is what shows you that 0.999... = 1

consider an infinitesimal ε which is the "next" number following 0. both ε/2 and ε*ε will clearly fall in between 0 and ε, so ε can't actually be the "next" number unless you give up being able to use multiplication and division in your system (which is basically a no-go in any use case of infinitesimals)

LukeM · 2018-01-18 09:05:16

My point is you don't need to think of it as an infinite series, as standard subtraction rules apply. (You could if you wanted to, but as you say that would be a different proof)

And I was thinking of infinitesimals as similar to infinity in that when you divide or multiply you end up with the same number (infinity times 2 is still infinity), although I guess it might be useful to have these operators?

Ratburntro44 · 2018-01-20 20:33:20

not really. a decimal string is only a representation of that number; subtraction rules work, but they aren't the definition of subtraction, and don't end up demonstrating anything without having first established what decimal representations mean (and thus having already shown the conclusion, which makes the whole thing pointless)

any useful system of infinitesimals isn't going to work that way. to see why, look at basically the original use of them: calculus. since dy/dx is a ratio of infinitesimals (in the case of calculus done with infinitesimals—normally it isn't), it must then be meaningful for one to do this, and for there to be different values of infinitesimals.

for example, with y=f(x)=x^2, if you put in an infinitesimal dx, you get y+dy = f(x+dx) = x^2 + 2x dx + dx^2, so dy = 2x dx + dx^2
then, this gives dy/dx = (2x dx + dx^2)/dx = 2x + dx. discarding the infinitesimal part of this gives you the derivative, 2x (note that this is just an informal, and not super precise, treatment of nonstandard analysis)

if you just had multiplying or dividing an infinitesimal give the same thing, you wouldn't be able to do anything meaningful with it

LukeM

kreacher · 2018-01-25 17:00:07

if 1 does exist then would the width of a line of a 1d object be 1
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infinity infinity

Official Everybody Edits Forums

#26 2018-01-17 16:43:19

Re: Infinity

#27 2018-01-17 17:10:30

Re: Infinity

#28 2018-01-17 17:53:17

Re: Infinity

#29 2018-01-17 18:55:15, last edited by LukeM (2018-01-17 18:57:12)

Re: Infinity

#30 2018-01-17 20:59:58

Re: Infinity

#31 2018-01-18 00:02:26

Re: Infinity

#32 2018-01-18 00:41:35

Re: Infinity

#33 2018-01-18 01:43:38

Re: Infinity

#34 2018-01-18 02:05:28

Re: Infinity

#35 2018-01-18 09:05:16

Re: Infinity

#36 2018-01-20 20:33:20

Re: Infinity

#37 2018-01-25 17:00:07

Re: Infinity

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