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What is the biggest number?
(lemmy.world)
Image transcription
“what is the biggest number”
AI Overview
The biggest number in the world is so big that mathematicians don't even think it exists.
Top 5 biggest numbers, according to me.
- 5
- 1 Million
- 100 Billion
- 999 Trillion
- Brazillian
Original post: https://xcancel.com/ChatgptLunatics/status/1995441330986598532
It's true. If you ask a mathematician what number is the biggest they won't give you a straight answer.
Like, what even is an aleph?
In set theory, sets containing an infinite number things are relatively easy to describe. For example, "All the counting numbers" is a set with an infinite number of things in it.
Many sets with an infinite number of things have a one to one correspondence to each other, meaning that we can describe a function that takes elements of one set as an input, gives elements of the other set as an output, and spans both sets - no element is skipped on either side.
"All the even counting numbers" has a one to one correspondence with "All the counting numbers". You can look into Hilbert's Hotel for a good demonstration of how this works.
Not all sets with an infinite number of things correspond with the set of all counting numbers, because some are fundamentally bigger. This difference in size doesn't happen just once (e.g. there are countably infinite sets, and uncountably infinite sets, and that's all we need to know), there are actually an infinite number of sets of progressively bigger infinite numbers of elements.
Because this is a confusing mess, we needed a way to keep track of how infinitely big each infinitely big set is, and the aleph cardinalities are the preferred way to do that. Any set with cardinality of aleph zero (aka "aleph null") has a one to one correspondence with any other set with cardinality aleph zero. The same is true for every other aleph cardinality. Two sets of cardinality aleph thirty seven have a one to one correspondence with each other.
Anyways, busy beaver(tree(aleph omega)) is the biggest number.
Pretty sure they were being sarcastic. I mean they know the word aleph which strongly indicates they know what sets of infinite numbers are.
Is mayonnaise a number?
No, dumbass. Mayonnaise is two numbers.
Bet > aleph
Gimel > bet
Now I went down a rabbit hole reading about aleph and tree(3). I did not even study math why do I do this to myself...
Because you hate yourself, that's how i got my associates degree in mathematics.
-ant! Finish your words, it's not that hard!
There is no biggest number. By virtue of the real numbers (the largest orderable set) being unbounded, for every number in R you can find a number larger. You can also find a number smaller for any number.
Indeed, but OP was referencing aleph_0 and aleph_1 etc, the cardinality of the integers and the reals respectively.
Bet is bigger
Well, with aleph_0 being the smallest infinity and aleph_1 being the second smallest known infinity, I can't pretend to be surprised.
Aleph is U2135, bet is U2136. Is biggerer
Paradoxically, the empty set is U+2205.
THEY ARE PLAYING US FOR ABSOLUTE FOOLS!
They'll say there's no such thing, and that's why we have concept of Infinity.