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Simply Beautiful Art
Simply Beautiful Art
13:14
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Q: Proving Topological Equivalence without finding a function

NilknarfMy topology book defines topological equivalence as Two metric spaces $(A,d_A)$ and $(B,d_B)$ are topologically equivalent if there are inverse functions $f:A\to B$ and $g:B\to A$ such that $f$ and $g$ are both continuous. I've been using this definition to prove topological equivalence, bu...

general-topology continuity alternative-proof
Lol
@Nilknarf I mean, I can do them, but I certainly don't do them regularly
Simply Beautiful Art
Simply Beautiful Art
14:13
@user462339 Haha, yeah. The key to making my rooms somewhat flourish is keeping them open to many topics, letting them range in conversations from casual to serious stuff, though mostly casual... people do not want to come to rooms with a "laser like focus"
4
 
2 hours later…
Annelise t.
Annelise t.
15:52
@aminliverpool I'll promote this good idea on my profile. :)
 
6 hours later…
Simply Beautiful Art
Simply Beautiful Art
22:02
Lol, this room actually happened.
well...
I do all things series related
most of calculus/analysis stuff
But if anyone is really interested, I'll teach them googology :)
@Anneliset. >.> Probably not me right there
@aminliverpool Lol, I think you are almost too serious about this...
Annelise t.
Annelise t.
22:24
@SimplyBeautifulArt hahah come on, we all know how to googology (I think you mean to google things about math) but there are some exercise that need the help from the experts, google isn't enough
Simply Beautiful Art
Simply Beautiful Art
@Anneliset. googology.wikia.com/wiki/Googology_Wiki
Annelise t.
Annelise t.
oh I think you are one of them haha,jk I haven't observe your behavior here on MSE
Simply Beautiful Art
Simply Beautiful Art
googology.wikia.com/wiki/Googology
"Googology is the study and nomenclature of large numbers"
Annelise t.
Annelise t.
Oh
I see
Simply Beautiful Art
Simply Beautiful Art
What's the largest finite number you can describe in about 20 symbols?
:) If you want the challenge
Using only basic symbols like addition, multiplication, etc. and any symbols you care to define yourself
Annelise t.
Annelise t.
22:29
999...9! 20 times, is that what you mean?
or did I misunderstand the problem?
Simply Beautiful Art
Simply Beautiful Art
Sure, but I can go even bigger in about 5 simple symbols
9^(9^9)
7 symbols lol
Annelise t.
Annelise t.
is it bigger than mine?
Simply Beautiful Art
Simply Beautiful Art
Yes
Annelise t.
Annelise t.
I have 19 nines and one !
Simply Beautiful Art
Simply Beautiful Art
Hm... wait, lemme think
Perhaps I need one more symbol....
9^(9^99)
there we go, definitely bigger lol
I see you've changed your pfp
Annelise t.
Annelise t.
22:33
haha mathematica explote with your number
what is pfp?
Simply Beautiful Art
Simply Beautiful Art
profile pic
Annelise t.
Annelise t.
yes, hours ago
Simply Beautiful Art
Simply Beautiful Art
lol, well it just showed up for me now
chat can be a bit behind the main sites
Annelise t.
Annelise t.
really?
Simply Beautiful Art
Simply Beautiful Art
:P Yea
So, can you make anything bigger with 20 symbols?
Annelise t.
Annelise t.
22:38
but also exploted with mine
Simply Beautiful Art
Simply Beautiful Art
ofc
computers aren't meant to handle these numbers until we start talking theoretical computers
Annelise t.
Annelise t.
9^(9^99999999999999)
there
20 symbols
Simply Beautiful Art
Simply Beautiful Art
9^(9^(9^99)) is larger in less symbols
Annelise t.
Annelise t.
9^(9^(9^(9^(9^(9^9))
20
Simply Beautiful Art
Simply Beautiful Art
Yup, and that's likely the limit
Now raise the bar to 50 symbols?
@Anneliset. Do you know any programming languages?
Annelise t.
Annelise t.
22:45
to 50, the patter is the same 9^(9^(9^(9^(9^(9^9...)) isn't it?
Simply Beautiful Art
Simply Beautiful Art
f(0)=9
f(n+1)=9^f(n)
f(100)
Annelise t.
Annelise t.
why? I'm learning to program
Simply Beautiful Art
Simply Beautiful Art
this is much bigger and in less than 50 symbols
Sometimes programming languages can write this stuff in less symbols than you might normally manage
Anyways, my number is equal to 9^(9^(...101 9's...))
Annelise t.
Annelise t.
:) nice tricks, right?
Simply Beautiful Art
Simply Beautiful Art
Nah, this stuff is very small compared to the numbers I can write
In 100 symbols of Ruby, I can write numbers as large as $f_{\omega^3}(n)$ in the fast growing hierarchy
In about 230 symbols of Ruby, I can write numbers as large as $f_{\Gamma_0}(n)$, where $\Gamma_0$ is the Feferman something something ordinal.
Annelise t.
Annelise t.
22:55
I have no idea about your functions, Gamma omega, I suppose some day I'll study them
Simply Beautiful Art
Simply Beautiful Art
:P
Hello @PVAL-inactive
Let's just say very very large numbers. Want to learn about them? XD
Simply Beautiful Art
Simply Beautiful Art
23:51
D: Where's all duh people

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