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Tuesday 08 April 2025 20:52:56 GMT
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some random account :
ℵ0 aleph-null Also known colloquially as infinity. In Cantor's theory of transfinites it is known as aleph-null when treated as a cardinal number, and omega when treated as an ordinal number. In an informal sense all of these concepts are the same, but there are important technical distinctions to be made. Infinity in calculus refers to a real quantity which increases without bound. It is not so much a number, as a way of expressing the behavior of a limit. omega refers to the order-type of the set of non-negative integers. Aleph-null on the other hand, is defined as the cardinality of the set of positive integers. In plain speak Aleph-null is the "number" of numbers. The problem with this is that the set of positive integers is suppose to represent all things that we might wish to count. It however, can not count itself. So is the "number" of numbers, even a number then? Cantor thought so. In some ways we can treat aleph-null as a number, in that we can compare it to other numbers and determine which is larger. Using the concept of one-to-one correspondence Cantor showed that we can rationally say that aleph-null is larger than any positive integer, even though the previously prevailing wisdom was that infinity was not a number and could not be compared in this way. But accepting this view leads to some mind bending anomalies. Using one-to-one correspondence we can show there are just as many even numbers, squares, cubes, etc. as there are positive integers, despite that fact that these are all subsets of the positive integers. This violates the principle that the "whole is always greater than any proper part of the whole". So aleph-null is a number such that a proper part of it is still just as large... baffling. When working with finite numbers we implicitly understand the exclusivity of "larger" vs. "equal". A number can not be both. Hence when one particular correspondence shows that one finite set has more than another finite set, we know that no correspondence can exist which shows they are equal. Not so with infinite sets! Even if we have a correspondence which shows one is larger than the other, it doesn't necessarily mean that a correspo
2025-06-28 18:22:51
0
😬 :
e_lol IS NOT TOP 1? LAST TIME IVE PLAYED THIS HE WAS WTH
2025-04-08 21:36:29
1247
M1ST4K3 :
what happened to e_lol bro😭
2025-07-02 12:28:38
0
Ayden🗣 :
e_lol's downfall NEEDS to be studied😭🙏
2025-06-03 14:35:42
846
Ali :
he might aswell quit until 2030 and still be 1st💔
2025-04-09 13:30:36
1618
𝓚𝓲𝓻🌹 :
e_lol not playing no more but still top 8🔥
2025-07-07 15:25:02
0
zenelik :
fun fact he is hacking (seriously)
2025-04-09 10:34:54
191
𝘜𝘵𝘰𝘺!🫨🙈 :
where's e_lol? bro 💔💔💔
2025-06-06 15:45:12
0
Goth mommy discharge jar 🫙 :
bro the difference between 2nd and 1st is 700 quadrillion 🥀
2025-04-10 17:19:06
453
RedLobster 7 OZ Sirloin Meal :
Can’t even hit 10B 🥀💔
2025-07-04 15:57:43
0
jahseh :
what country is this
2025-07-06 01:51:06
0
gurt :
I don’t think havingfun is having fun anymore
2025-04-09 05:04:27
2819
like if you're not gay :
read my name
2025-06-19 11:11:55
3
🎭 :
Ethanolodj is the wallhop guy and the glitches
2025-06-03 09:32:09
1
Sussy baka :
i still thought sdmittens is top 1 🌹💔🥀
2025-07-06 14:20:44
0
Thanh / NR 6 Spamton glazer :
BSS is NOT that fun 😭🙏
2025-06-03 13:12:37
22
⠀ :
i can't even hit 1T 💔💔
2025-05-25 03:42:21
29
Gifted lion bee 2.0 :
e_lol at 8th💔
2025-06-03 08:49:12
0
murasakibara :
why is e lol 8
2025-07-14 19:03:58
0
Animowany :
they just macro 27/7,i feel bad for they pc
2025-04-10 06:53:05
339
͒ :
me with 1b ........
2025-04-09 12:11:18
1
gtw :
e_lol at 8 looks cursed
2025-06-07 06:33:53
1
twodfr :
i got 1.0041 quintillion but frogot to record
2025-06-05 13:20:29
1
Rb :
I have 12 bill in 2 days gametime is that good?
2025-04-09 18:47:49
0
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