this defines my favorite function

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this defines my favorite function

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Күн бұрын

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Пікірлер: 66

@The-Devils-Advocate Ай бұрын

The thumbnail is a bit confusing

@cosimobaldi03 Ай бұрын

Definetly

@michaelrogers4834 Ай бұрын

Oh, thank God! The thumbnail had me questioning all of reality.

@paulius9351 Ай бұрын

You know you're a real fan when you immediately realise the function is the floor function only from the video's title.

@rmlu9767 Ай бұрын

Nooo! You spoiled me the video.

@9WEAVER9 Ай бұрын

I guess I'm a real fan and I just didn't know it, because I check every day for uploads but I didn't recognize the inequality as specifying the floor function.

@urisinger3412 Ай бұрын

why is this the top comment, fucking spoilers

@coc235 Ай бұрын

@@9WEAVER9It's not about the inequality, but rather fhe video's title.

@shirou9790 Ай бұрын

I think I was able to guess from the statement alone. The inequality makes it look like the function is sort of linear (with an error of about 1 unit at most), and it also specified that f(x)

@walidability Ай бұрын

I always like functional problems

@hassanalihusseini1717 Ай бұрын

Yesa, I like them, too. But I am not good at solving most of the time.

@ayanokojiuchiha6877 Ай бұрын

@@hassanalihusseini1717 they are fun

@goodplacetostop2973 Ай бұрын

16:58 I know the answer and I won’t give it, but yeah that’s a classic from Michael 😂

@TheDannyAwesome Ай бұрын

Question: If you change the values in the orange condition, what (family of) function(s) do you get? If you remove the green condition, what family of functions do you get? If you remove the former blue inequality, what family of functions do you get? If you remove the latter blue inequality what family of functions do you get? Are any of these questions realistically answerable?

@Kettwiesel25 Ай бұрын

I asked myself the same questions and have some partial answers. There are other solutions then. If, for instance, you drop the red condition, you can multiply by any element a

@peterluger1400 Ай бұрын

try it yourself

@gordontan2092 Ай бұрын

So there is just 1 function that satisfies the criterias and it is the floor function?

@lyrimetacurl0 Ай бұрын

y=x also works, right?

@bigfgreatsword Ай бұрын

@@lyrimetacurl0not quite... There's the not-in-thumbnail inequality 2

@eveeeon341 Ай бұрын

I never really understood why the floor function was his favourite. But now he's converted me to a floor function enjoyer, functional equations always delight me and this was a particularly beautiful one!

@wides1982 Ай бұрын

Cool proof and amazing presentation. Thanks!

@looney1023 Ай бұрын

Did we prove that this is the only function that satisfies this property?

@klausolekristiansen2960 Ай бұрын

Yes.

@peterluger1400 Ай бұрын

technically he only proved that if a function with these properties exist, then it must be the floor function. however it is rather easy to see that the floor function indeed satisfies the stated conditions

@lucianoxiccato5458 Ай бұрын

I belive the cover of the video is wrong

@assassin01620 Ай бұрын

I thought it was wrong at first, too. I had to analyze it a bit to understand. Lol I think swapping "f(x) + f(y) + 1" and "f(x) + f(y)" and flipping the inequalities would make it less confusing.

@yuseifudo6075 Ай бұрын

It's not

@lucianoxiccato5458 Ай бұрын

@@assassin01620 it is saying that f(x)+f(y)+1

@assassin01620 Ай бұрын

@@lucianoxiccato5458 The red arrows are telling you where to place the "f(x) + f(y) + 1" and the "f(x) + f(y)". So it's saying: "f(x) + f(y)

@lucianoxiccato5458 Ай бұрын

@@assassin01620 AHHHHH sorry but that was confusiong ahah

@frimi8593 Ай бұрын

The floor here seems to be made out of floor

@jonathantorres913 Ай бұрын

Loved the use of its period at the end of the proof!

@moonwatcher2001 Ай бұрын

Interesting, amene, and very well explained. Thanks❤

@zzzzzz-qo1cg Ай бұрын

Biggest ever clickbait on the cover

@DerQwertzu17 29 күн бұрын

Cool video, but dont you still have to proove that floor(x) fulfills those conditions?

@adamluter Ай бұрын

Not a big deal, but the card has the greater thans flipped?

@MrStanny32 Ай бұрын

you're missing the red arrows

@adamluter Ай бұрын

@@MrStanny32 indeed I did. I think reversing the three lines would be clearer still.

@orisphera 29 күн бұрын

I started by substituting 0 for y. I didn't substitute anything specific for x in this

@RASCAL011 Ай бұрын

Congratulations sir for 300k subscribers . You are my one of the favourite maths teacher ❤

@JCCyC Ай бұрын

OH NO. I SMELL FLOOR. (Paused at 11:19)

@talastra Ай бұрын

More new stuff!

@louisreinitz5642 Ай бұрын

Just one glance tells me it's the floor function (let's see the proof and whether I'm right)

@MrRyanroberson1 Ай бұрын

I think the extra two assumptions are too specific to feel like it's some natural thing, most wspeciall the second one. If you assume f is increasing, then saying [0,1) all

@Blabla0124 Ай бұрын

You didn't need to prove f(x) = -1 for x in (-1,0) I think?

@thenationalist8845 Ай бұрын

12:58 I know the answer now 😃 Yay Watch complete video 🎉

@Thomas154321 Ай бұрын

What symbol are you using instead of &? It looks like the number 3 with a dot above and below. Is this something people are generally familiar with?

@frallan874 Ай бұрын

Just a variation of the & symbol, used within linguistics too in some cases. Which one to use is usually just up to the preference of whoever's writing it.

@ChefSalad Ай бұрын

As is said below, that's just a graphical variant of the ampersand symbol. The ampersand symbol is just a digraph (read: combination that retains the original order) of "et", the Latin word for "and". That variant symbol is really supposed to be an E with the two lines above and below representing the t, but, for some unknown reason Michael wrote the symbol backward. (Yes, they aren't really dots, but small line segments, kind of like how some people don't put a full line through the S when writing a $, but just put little lines on the top and bottom of the symbol.). There's another variant that's sometimes used that is literally just a curvy Et, with the bottoms joined together (It helps if you use the lowercase t with the serif on the bottom, like in the font KZbin uses, but flipped the other way around.). If you write that and kind of tilt the top of the T leftward a little, then you'll get an ampersand. Also, I'd like to point out that the name "ampersand" comes from two facts: one is that the ampersand used to be considered an actual letter of the alphabet in English, and the second is the Alphabet Song. In the song, the last letter was the ampersand, but it was originally called "per se and". "Per se" is Latin for "for itself", so "per se and" meant the symbol was the word "and" in its own right. Since "per se and" was the last letter of the alphabet, the song ended with the words "and per se and", which eventually was re-bracketed and shortened to "ampersand".