Mathematical closure

Understanding what it means for a set to be closed under an operation.

[skankhunt-zhmo]

Thanks, I started with you for algebra 1 and now im in discrete math

[thefitsbitcrown]

This guy is amazing, he has always helped me with my math issues. God bless him.

[kodisoma]

Some of the best explanations allll over the world 🌎!!! Thanks for khan

[Cunch]

Thanks, that helps a lot in understanding how to tackle proofs

[livelaughloving]

thank god my teacher was like “figure it out yourself” so here i am

[thelegendaryeagle]

how do you right so good with your mouse on desktop

[medhatmostafa]

Can you do group theory? I'm taking further maths A level and it will be really useful, thanks for the awesome videos!

[-_Nuke_-]

I know that Complex Numbers are closed under all possible operations but what about dividing by zero? That is undefined ofcourse but then what about mathematical closure? Does 1/0 render mathematics not closed or is the "undefined" answer sufficient enough?

Because before imaginary numbers, the sqr(-1) was also undefined, until it was defined to be the number i. Is that a hint that mathematics are not closed even in the level of complex numbers because of this 1/0 problem? Or it being undefined solves our problem forever?

[layanosama]

i understand.. but im a bit lost with the division part. i mean, what if i say: 2/1=1. isnt that closed??? 1 is an integer, right??? so how does this work!!!

[gunamaypal]

Pls discuss with example in real life of real analysis every thing. I want to say pls discuss in broad view, ignited mind

[matthewjames]

where can I see the proof of closure under addition? Great video btw!

[austinchen]

on my text book it says when performing the operation on any 2 numbers in the set, will result in another number in the set. So does that mean in this situation you could also do c+a=b?

[subratabiswas]

Whole numbers are not closed under substraction

[connorgrady]

Why isn't this on khan academy's website?

[eleanoradams]

im in 7th grade and we have to know all about closure FML

[joymatideviakupdevi]

I don't know this kind of English

[sp_ligmasp_clan]

1:25 leave a like on this comment if you understood👌😂

[albinsopaj]

I believe Sal made a mistake when he assumed that Natural Numbers (Integers) are closed under subtraction. It's not the case that if you take two integers and subtract them from one another, the result is another integer. Take 2 and for 4. 4 - 2 = 2, but 2-4= -2 and -2 isn't an integer. Therefore, the conclusion is that Natural Numbers are only closed on ADDITION and MULTIPLICATION.