/sci/ - Science & Math

infinity - 1/infinity

>>4743943
that's it, nothing more to see in this thread, move along folks

>>4743942
infinity - (1/infinity)/infinity

>>4743957
infinity^infinity-1/(infinity^infinity)

>>4743961
infinity = infinity^infinity, since by definition infinity is the biggest number ever.

Same thing with (1/infinity)/infinity, you already divided by infinity, you can't make that shit any smaller bro.

Infinity

Minus 1.

>>4743948
>>4743943

>implying you can perform arithmetic operations on infinity

>>4743942
x = Largest finite number

x+1

/thread.

bump for le gusta face

>>4743973
>largest finite number
> x+1

full retard

>>4743978
U mad I pwnt you by definition?

>>4743977
lol lel xDDDDD

LE REDDIT LE COMEDIC LE GURLD

XDDDDDDDDDDDDDDDDD

>>4743972
sure you can:

infinity/infinity=1

>>4743980
what he is saying is that you have a fatal flaw in logic. If obtainable, adding anything positive to the largest finite number would make it infinite.

>>4743982

Infinity isn't a number. Division isn't a valid operation on non-numbers.

>>4743986
THat's what you say now, but when I divide the universe an infinite number of times, you're going to be sorry.

The largest finite number, <span class="math">\kappa_{\bar{0}}[/spoiler], is approximately 3.2371... [Mann 2010]. A simple expression is not presently known; the best we have is an ugly set of recursive equations I'm not going to bother transcribing that converge at something like <span class="math">\mathcal{O}(\log n \log \log n)[/spoiler].

It has been shown that <span class="math">\kappa_{\bar{0}}[/spoiler] is transcendental, assuming the Riemann Zeta Hypothesis [Paradowski and Adams, 2009].

>>4743984
Yo dawg I heard you like recursive definitions so we put a recursive definition in your recursive definition so you can contemplate paradoxes while you contemplate paradoxes.

Archimidean principle.
/thread

>What is the largest finite number?

I'm not sure, so I will call it Q.

All real numbers are finite, so Q is greater than x for all real x.

Either Q is real or Q is not real.

For all reals x + 1 > x.

If x = Q, Q + 1 > Q which cannot possibly be true because Q is greater than all reals, so Q is not a real number.

All numbers expressible in finite decimal notation (e.g. 123.456...) are real, but Q is not.

Numbers like <span class="math">\frac{1}{3}[/spoiler] have an infinite number of numbers to the right of the decimal point.

Perhaps Q has an infinite number of numbers to the LEFT of the decimal point? (e.g. 111...111.456...)

That could leave infinite possible values for Q (e.g. 111...111.35 or 4343.....43.142857...)

Q is not uniquely determined.

[FIX THE FUCKING SYS.4CHAN LAG PL0X WHILE I SPAM CLICK SUBMIT]

>>4744031
>Perhaps Q has an infinite number of numbers to the LEFT of the decimal point?

I'm not going to call you wrong, it's just that your question made me think of "Don't all numbers have an infinite number of numbers to the left of the decimal point?"

000001 = 1

its propably 4 or something close to that.

There is obviosly no largest number in the set of reals or it's unbounded subsets.

In contemporary mathematics, people introduce other numbers to get a grasp of the size of certain sets and there you find very very very big numbers

http://en.wikipedia.org/wiki/Large_cardinals

I remember there actually being a wiki for keeping track of those

http://cantorsattic.info/Cantor%27s_Attic

On a related note, there is this youtube channel which recently made a video on Grahams number

http://www.youtube.com/watch?v=XTeJ64KD5cg

and on a less related note, for those who are interested, there is a channel for physics topics in the same vain

http://www.youtube.com/watch?v=0mgXNgD3JFU

>>4744256
this is what rabbit actually think

>>4743943
<span class="math">\infty - \dfrac{1}{\infty}[/spoiler] is technically still infinity.

>>4746158
<span class="math">>>4743943
<span class="math">\infty - \frac{1}{\infty}[/spoiler] is technically still infinity.[/spoiler]

>>4746161
Fuck TeX

∞ - (1/∞) is technically still infinity.

googol

>>4746158
>>4746171
use this:
http://www.codecogs.com/latex/eqneditor.php

you can sample your latex output to see what it'l look like before you post, and then just copy paste it into the reply field.

>>4747011
function buttons at the top as well, so you can latex like a pro even if you cant remember all the commands.
<<<
also, kudos to josef for this.

>>4743942
Suppose there were a largest finite number. Call it n, but n+1 is finite and larger than n, therefore there is no largest finite number.

>>4746171
Don't fuck TeX, fuck 4chan's implementation of it. dfrac got me the other day too.

>>4747011
Doesn't solve the problem. Various commands are unavailable on 4chan, such as dfrac. Any tex editor will be fine with it, not 4chan though.

>>4747021
>>4747025
you could e-mail moot?
a fix wouldnt be that hard, surely?

>>4747032
I believe many of them were removed purposely, to prevent the use of TeX in board spamming.

For every real number r, I can find a natural number n so that: n>r.

And for every natural number n I can find a natural number m:=n+1 with n<m.

There is no greatest number, why do these threads always get so many replies? ;_;

>>4743942

Infinity by definition, is not a number, it's a concept. This whole fucking thread and its replies are fucking stupid, get off /sci/

>inb4 adding to and bumping thread with my own reply hurr durr

>>4747152
http://en.wikipedia.org/wiki/Cardinal_number

>>4747036
ah yes, that triangle thing /jewcommand something something...
i remember that

fucking crahed my internet every single time

Gram's Number is supposedly the largest single number

>>4747170
http://en.wikipedia.org/wiki/Graham's_number

>>4747171
>>4747170
wow
grahams number is awesome

"Indeed, the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies at least one Planck volume."

>>4747170
graham's number + 1 wants a word with you