𝝒𝝆

21, math student.

[𝝒𝝆 @kac3pro]

@FoxGhos83810720 No racja. To nie wiem

[𝝒𝝆 @kac3pro]

@FoxGhos83810720 Jeśliby chcieć to robić tak to chyba najlepsze co mogę zaproponować to coś takiego: Niech B będzie rodzina wszystkich zbieżnych podciągów a. Rozważmy c=a\⋃ B. Albo c jest skończony i koniec albo nie mam żadnych podciągów zbieżnych I sprzeczność.

[𝝒𝝆 @kac3pro]

@FoxGhos83810720 A no wtedy jest ok. Przez kontrapozycje a-/>x więc istnieje podciąg b' elementów taki że ||b'_n-x||>eps dla pewnego eps>0. Ze zwartości b' ma podciąg zbieżny b, ale b nie może zbiegać do x.

[𝝒𝝆 @kac3pro]

@Karol1669024 @pangram ai?

[𝝒𝝆 @kac3pro]

@DoozerDiffuser @SuperheroFreak Technically yes. For example 0.1999..
=0.2, but it is true that each number has a unique decimal representation that doesn't end with an infinite sequence of 9's. This fact is used in the cantors diagonal argument that the set of real numbers is uncountable.

[𝝒𝝆 @kac3pro]

@SuperheroFreak You say that truth is not a belief. Can you give me an example of a true statement?

[𝝒𝝆 @kac3pro]

@SuperheroFreak The stipulation is that you believe that 0.999.... is a number. If you do not accept that you can sum an infinite number of terms to get a finite answer then there is nothing to talk about. If you do however (as does almost everyone) then you have to also believe that 0.999...=1

[𝝒𝝆 @kac3pro]

@fchollet Are you saying not all real numbers are decimal numbers? Not even all rational numbers? That seems dubious

[𝝒𝝆 @kac3pro]

@alz_zyd_ If you read baby rudin and don't know what a function is then you should stop reading baby rudin. It's okay to be terse when you introduce the stuff the reader should be familiar with anyways. There are much bigger problems with how rudin is written so you are in for a ride.

[𝝒𝝆 @kac3pro]

@alz_zyd_ It's useful to have a symbol for saying "for all" because it's so common. It's the same as writing = instead of the word equals.

[𝝒𝝆 @kac3pro]

@garvvee @keysmashbandit Yeah same here. This is horrible.

[𝝒𝝆 @kac3pro]

@Almost_Sure @Lptomov82 As in elementary proofs exist at all. It is still not easy and I don't know of any elementary proof that's not tedious.

[𝝒𝝆 @kac3pro]

@AcerFur @littmath How would an amateur be able to judge whether the output is slop or not though?

[𝝒𝝆 @kac3pro]

@Rafa_Schwinger @predict_addict Well about half were on the imo already in high school, and surely their mathematical abilities have vastly improved since then. Perhaps they would need to brush up on a few things but I believe the vast majority should be able to get a medal without any problems.

[𝝒𝝆 @kac3pro]

@bill_2023_evans @davidbessis This take is completely backwards. The job of a mathematician is to understand maths, not to prove theorems. Proving theorems is the means, the goal is and always will be understanding.

[𝝒𝝆 @kac3pro]

@FlipMeAC Jesus the comments under OP are so retarded.

[𝝒𝝆 @kac3pro]

@kendrictonn Or rather "te kalliste".