Alexa

𝚜 𝚕 𝚎 𝚎 𝚙 𝚎 𝚛 @sleepyposs.bsky.social [ View ] May 05, 2024 at 17:16 UTC

c o m m u n i o n

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Alexa @alexaisabird.bsky.social [ View ] May 03, 2024 at 03:21 UTC

i have this exact same problem

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Alexa @alexaisabird.bsky.social [ View ] May 01, 2024 at 06:05 UTC

Yeah, we're thinking "how many things are there in this set" rather than "how much do they sum up to", because any sum of the absolute value of a numerical set will approach infinity.

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Alexa @alexaisabird.bsky.social [ View ] May 01, 2024 at 00:34 UTC

No, the irrational numbers are a larger infinity. The sum of all rationals or the sum of all irrationals does not play a part in this. We're just thinking about how many things there are in each set.

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 18:24 UTC

DRACULA FLOW 5 LET'S FUCKING GO

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 18:18 UTC

Absolutely, no problem! This stuff is super hard to understand, I even was sanity checking my own knowledge to make sure I wasn't getting anything wrong. It's really unintuitive and strange!

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 15:43 UTC

I hope this makes a bit more sense? We're not talking about blocks in buckets, but more how "dense" the elements are in buckets. Here's a video from Numberphile on this as well: www.youtube.com/watch?v=elvO...

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 15:41 UTC

2. I'm not saying that each irrational number is its own infinity, but rather that there are infinititely more irrational numbers than there are rational numbers. You can think of the bucket containing all irrational numbers being more "dense" than the one with the rational numbers in them.

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 15:40 UTC

If something is both injective and surjective, it's called "bijective", which means that you can tie everything from one bucket to exactly one other thing from the other bucket of our buckets of things. If we can tie objects together like that, they're the same size.

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 15:38 UTC

If you have to tie 2 or more things from one bucket to the same thing in another bucket to tie every thing in each bucket together, the function is "surjective". If you tie everything from one bucket, even if the other bucket has things that aren't tied to anything, it's "injective".

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 15:35 UTC

Most sets can be "mapped" to other sets, like tying a piece of string between two objects in buckets. The way the string ties a thing from one bucket to a thing in another bucket is a function.

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 08:14 UTC

This concludes this particular Alexa Special Interest that she is spending years of her life studying and is very passionate about moment. Thank you for tuning in, folks.

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 08:11 UTC

To check this, you can take any arbitrarily large number x, and see that there will always exist a number 2x that is even, and vice versa, where you can take an arbitrarily large even number x, and see that there is a number x/2 that is a whole number. Doesn't matter what number x you choose.

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 08:06 UTC

In easier terms: An infinity is bigger than another infinity if you cannot connect each thing in one infinity to another thing in each infinity, and have every thing in each infinity connected this way. That's the simplest way to explain a bijection my brain can think of atm.

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 08:01 UTC

A set can be a strict subset of another subset and still be the same size. Infinity is weird.

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 08:00 UTC

Two infinities are the same if there exists a bijection between their sets. For example, from whole numbers to even numbers, just do f(x) : x -> 2x. This trivially maps the whole numbers into the even numbers.

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 07:59 UTC

We term this the cardinality of the infinity, essentially how "big" it is, and the irrational numbers and real numbers are uncountable infinities, while the integers, whole numbers, natural numbers, and rational numbers are all "countable" infinities.

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 07:57 UTC

Cantor's diagonal argument is a good way to show how. You can assume that you can list every irrational number, but take a digit from each and change it by 1, and get an irrational number that must be different from any of the ones you have written down, and thus they are "uncountable."

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Alexa @alexaisabird.bsky.social [ View ] Apr 30, 2024 at 07:55 UTC

This is not true? There are the same number of numbers in all whole numbers as there are in all even numbers, there exists a bijection between the two, and that's trivial. There are more irrational numbers than there are rational numbers, though, which are different sized infinities.

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