Proof that f(x) = 1/x is not Uniformly Continuous on (0,1)

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You are literally my saviour. My exam is in few hours, and I just found your channel this morning. Thank you so much for providing such examples so it becomes easier to decipher what sometimes the book is trying to tell.

Edit: I passed my exam, and I am doing Real Analysis II this semester. Thank you very much.

hashbrowncookie

very helpful but i still don't understand at all how to realize which values i should choose for epsilon, x and y in each case, is there some kind of general criteria?

laflaca

You should stop making videos... If you're gonna just pick values without showing the scratch work of how to get them by ourselves, it's a waste of time.

cesareborgia

Is there any restriction about choosing value of epsilon
What if I take epsilon = 10

akritibhardwaj

Can some one please tell why he said the x>1?

Iman

I have a question : in another video you show 1/x IS continuous from (0, infinity), but isn’t (0, 1) contained within (0, infinity), so why wouldn’t it also be continuous?! Thanks so much! Warning: I’m a noob to continuity!

MathCuriousity

prove that f(z) =1/(1-z) is not uniform continuous for z<1...
Is question ka solution mill skta h??

shahzadimathematics

Good afternoon, does anyone have the solution for the book on the integral of lenbesgue by Jhon Frank? if so, would appreciate it if you share it

doglassemario

Nice explanation sir....
But this function is continuous on (0, 1) or not

parthasarathy

EDIT: Disregard this comment just noticed that I am incorrect.

fietemicholka

Your definition of uniform continuity is missing the fact that delta should ONLY depend on epsilon! The definition you wrote is that of continuity!

fsm_grave

F(x)=1/x^2 is uniformly continuous on (0, 1)???? Plzz must reply

anniekhan

pretty basic videos. as a teacher you should really explain more about how you construct the argument, rather than just listing the steps of the solution, like a solution manual.

hope you improve in the future.

say-cred

Would it be possible to say that, since (0, 1) is not compact, the function cannot be uniformly continuous by Heine's Theorem?

Also, there is some critique in the comments on your video format... personally I really like the way you do things relatively quickly (please don't become like Khan academy who takes 20 minutes per problem) but it would probably be more helpful if you explained why you chose the values, instead of explaining straightforward algebra that all of us can figure out on our own.

Anyways, keep up the good work! Thank you!

vinvic

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