rx math
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Friday 04 July 2025 20:19:04 GMT
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k13pizzle :
It’s been a minute since my real analysis days…isn’t this concept called cardinality?
2025-07-04 20:27:21
25
Joshua Thooyavan :
"Oh sorry, your argument was disproved by the diagonal dog of despair and doom" 😓
2025-07-05 07:31:15
25
jacobsteele64 :
why can't we just add the new number to the bottom of our list?
2025-07-05 13:46:06
0
Huzi456 :
Vsause made video on this! “How to count past infinity”, for the people who want a long form explanation.
2025-07-05 04:55:10
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marco262 :
I finally wrapped my brain around the axiom of choice recently, and your video got me wondering: Does this proof rely on the axiom of choice? It seems like it would for you to be able to order the real numbers in any meaningful way.
2025-07-05 05:45:25
1
フランコ :
I’m familiar with Cantor and set theory, but stopped taking an interest in philosophy of mathematics when I got to Russel and Russel’s paradox. Can you give us an explanation oh how set theory overcame Russel’s argument?
2025-07-05 03:18:01
0
WilsonBK :
Why can we manipulate the left list but not the right (whole number) list by adding ….1 on the same way?
2025-07-08 05:30:01
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Goldeneyes :
Which infinity is bigger?
2025-08-01 17:42:42
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Rangsk :
I've always liked the proof that the rationals are countable
2025-07-27 14:21:53
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Taffec :
this analogy for 0-1 and 1-2 made more sense to me, and yet still brakes my brain that its true
2025-07-05 03:03:20
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nar00w :
The issue is people say there are bigger infinites and they mean "they contain more elements", not that an imagined final numerical value is bigger.
2025-07-05 00:37:05
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Juan :
aren't there duplicates used in the 0-1 Vs 0-2 set. eg 0.8 will appear in the 0-1 set once and then be referenced twice in the 0-2 list at 0.8 and corresponding 1.6 value
2025-07-26 19:17:08
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fawn_hoof :
Neat! When I commented on the other video to ask whether all sets could be transformed to be as large as each other, I was actually thinking that surely at some point, the transformations must fail. I guess it makes sense that sets of decimals vs. whole numbers is where that would happen because yeah, you can infinitely add numbers to the ends of decimals to make sure they never have a scalable relationship to a whole number. Cool stuff!!
2025-07-05 02:21:45
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krazo3 :
It's cool that the irrational numbers make this work. It's possible to map the natural numbers 1 to 1 to the rational numbers, aka fractions. Consequently there are "more" irrational decimal dogs between 0 and 1 than there are decimal dogs that can be represented as fractions. That was unexpected to me when i first encountered it.
2025-07-05 06:07:15
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Syasya :
😭😭😭
2025-07-07 15:05:56
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turingdegree :
thank you for 1) explaining we measure size by bijection and 2) explaining what proof by contradiction is. that being said, as usual I have a quibble: you have to worry about trailing 9s using your method, because of the no uniqueness of decimal representation. the usual work around is any 0s become 1s and any nonzeros become 0.
2025-07-29 11:31:25
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