Pretty good, but to be honest would be more interesting if you did a short proof why rational - rational = rational and rational / rational = rational. When you don't show the definition, prove those things and you just assume then it makes everything pretty obvious, but it is grounded on some strong assumptions. So don't take this personally, but I think that if someone proves something pretty elementary then this person shouldn't assume a lot, because it kinda misses the point of doing elementary maths (it is fun, but it cannot be close to being rigorous if it isn't coming from definitions and so on). And I'm not saying that I think it would be better if you did everything from definitions, but if you assume too much you make a short video which doesn't really show much thought process except some transformations and logic. Still glad you're doing math videos as it grows a niche, but a cool community so wish you luck!
Doesn't I mean the set of all imaginary numbers ? (Complex numbers with no real component) I feel like the set of all irrationnal numbers would just be R\Q
If x and y are rational then x+y and x*y are rational Assuming that a+t is rational then a+t-a is rational tis rational contradiction as by hipothesis t is irational. Assuming that t*ais rational. Then t*a*1/a= t is rational, contradiction.
I quickly read the text and misinterpreted at as the English word „at“ in bad English. For only the sum it would be correct what I said, but so, you are right of course.
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Nice video, extremely trivial stuff
Nice video, very well explained 👍
Pretty good, but to be honest would be more interesting if you did a short proof why rational - rational = rational and rational / rational = rational. When you don't show the definition, prove those things and you just assume then it makes everything pretty obvious, but it is grounded on some strong assumptions.
So don't take this personally, but I think that if someone proves something pretty elementary then this person shouldn't assume a lot, because it kinda misses the point of doing elementary maths (it is fun, but it cannot be close to being rigorous if it isn't coming from definitions and so on).
And I'm not saying that I think it would be better if you did everything from definitions, but if you assume too much you make a short video which doesn't really show much thought process except some transformations and logic.
Still glad you're doing math videos as it grows a niche, but a cool community so wish you luck!
Hey, thanks, man! I will definitely keep your comments in mind.
I overcomplicated the problem by a lot after seeing that. Tried it similar to the way that one would prove that root 2 is irrational.
If you are successful with that proof, I'd love to hear your argument!
Doesn't I mean the set of all imaginary numbers ? (Complex numbers with no real component) I feel like the set of all irrationnal numbers would just be R\Q
The set of irrational numbers is R-Q. R is a subset of the complex numbers.
There’s different notations and conventions, so yes and ho
If x and y are rational then
x+y and x*y are rational
Assuming that a+t is rational then a+t-a is rational tis rational contradiction as by hipothesis t is irational.
Assuming that t*ais rational.
Then t*a*1/a= t is rational, contradiction.
Proof by fucking obviousness
Is the proof obvious or the statement, or both?
@@snellbrosmathI think he met the statement. I thought the statement pretty obvious, but obvious statements are generally hard to prove.
I thought of the same proof. But by directly using the definition of rational i.e p/q. And the theorems about integers.
Would love to see it!
a can also be zero in order to make the sentence correct.
If a=0, then at would be rational.
I quickly read the text and misinterpreted at as the English word „at“ in bad English. For only the sum it would be correct what I said, but so, you are right of course.
@@thomaslangbein297 Please let me know if I am wrong about something in the future! I want to make sure I make accurate content.
@@snellbrosmath👍