Epsilon Delta Continuity (Example 6): 1/x

[@lucasfreire1090]

my teacher explained epsilon-delta proofs in a really confusing way, so I thank you so much for doing this series! You are literally a hero!

[@ShivanshTiwari-yn8wd]

I really like his enthusiasm in explaining the numerical. Thank you and keep up the good work

[@sangwonlee5669]

I just started my Advanced Calculus(Intro.Real analysis) course and this is a perfect material for previewing. I appreciate your lecture, Dr Peyam

[@drpeyam]

Thank you!!!

[@drpeyam]

You should check out my advanced calculus website: people.tamu.edu/~tabrizianpeyam/Math%20409/math409.html

[@sangwonlee5669]

@@drpeyam I cannot thank you enough for this fascinating professional free content!

[@Mryeo5354]

Im six videos into your continuity playlist and I really appreciate the practice. Thank you

[@drpeyam]

Thank you!!!

[@adityadwivedi4412]

@@drpeyam how is this 8 months old?

[@jamesbentonticer4706]

It's easy to binge watch his videos isn't it.

[@speckpackgamer]

Dr. Peyam i kiss your heart de idea with |a| >= -a is ingenious this is where i struggled in my proof but now you have explained it very well and i gave the video a like

[@drpeyam]

You’re welcome 😊

[@speedbird7587]

Thanks for the fantastic video. I got a better intuition about the pointwise vs. absolute convergence.

[@NihilistEmier]

I'm bad at maths that's why 2n + 2n is 4n(foreign) for me

[@wtt274]

A beautiful proof .Thank you sir for the great video !

[@rjbeatz]

Hey, I am studying as an Electrical Engineer and I love your videos!!! Also, do you have armenian or iranian roots? Cause your last name ends in ian

[@drpeyam]

Yep Iranian

[@adityadwivedi4412]

This reminded me of the proof that concave functions are continuous on open intervals

[@chato9327]

Thank you so much for your videos Dr Peyam =D

[@billyhadinata4644]

7:20 where do you find |x| > |xo|/2 ? thanks!

[@lordstevenson9619]

I would love a 3B1B visual proof of continuity and limits would be great if it’s possible.

[@drpeyam]

Already done, check out the playlist

[@yoav613]

you managed to show continuity by yourself! blackpen redpen needed pikachu

[@harrik2465]

Thank you, great videos!

[@juancamilochavesmuneton4601]

Why in the step 2, when you're showing that Delta really works, you use first |xo|/2 as Delta but then use the other Delta. My doubt is: if in the proof I say that |X-Xo|

[@weiwei92x]

Hi Dr Peyam, could you explain a bit more why we necessarily need step 2? By the end of step 1, we've already shown the choice of delta will satisfy epislon requirement, right? Or is that because epsilon can be anything, that's why there is a possibility that there exists an epsilon which invalidates our assuption of x-x0 less than x0/2 ?

[@drpeyam]

No in step 1 we found our guess for delta, it’s in step 2 where we show that our delta actually works

[@shashwat22072]

I gave u the 100th like sir❤❤

[@drpeyam]

Yay!!!

[@wanchoi407]

Hi, Dr. Peyam. Appreciate and like your lecture! Allow me ask a quick question for you. At 06:14, how do we know 2*|x-x_0|/|x_0|^2 is less than the epsilon?

[@drpeyam]

We set it less than epsilon, since that’s what we want, and this gives us our delta

[@johnbarnes4596]

why didn't you use Xo to be 3/2Xo

[@iqrarali4631]

Kindly explain limit x->0 squaroot of X .

[@drpeyam]

Already done

[@iqrarali4631]

@@drpeyam I couldn't find kindly share link if possible thanks

[@JasonOvalles]

Is this what you were looking for? kzbin.info/www/bejne/mpuWc3RvbruKrLM You can find it next time by looking at the videos in Dr Peyam's channel. He's pretty well organized with his videos and playlists!

[@MathCuriousity]

But I saw another video saying 1/x is not uniformly continuous for x belonging to open interval (0,1)! Your domain includes everything in 0,1 except 0. So why do you show uniform continuity here but yet the other video says it id not continuous ?! Thanks!

[@desertpointshacks6299]

1/x is continuous but not uniformly continuous on (0,1]. Uniform continuity is a stricter condition which is not always satisfied. Intuitively the reason it fails to be uniformly continuous is that its graph becomes arbitrarily steep as x approaches 0. There is no universal value of delta that will work for all values of x0 for any given epsilon.

[@theproofessayist8441]

Dr Peyam since you are a PDE expert - please do a video on the glorious crowning theorem of ODE and PDE analysis please: that is of course, the Sturm-Liouville Theorem! :)

[@drpeyam]

I don’t think it’s that important, I never use it

[@theproofessayist8441]

@@drpeyam Ah really? Then what in your view is the most important theorem in ODE/PDE?

[@adityadwivedi4412]

@@theproofessayist8441 no single result alone can do anything mathematics is much vast

[@drpeyam]

^ Exactly, pde is such a vast field, there is no fundamental theorem of pde

[@theproofessayist8441]

@@adityadwivedi4412 This reminds me so much of one of my math professor's commentary on the interpretation of Godel's Incompleteness Theorem as stated in Douglas Hofstadter's Godel Escher Bach Eternal Golden Braid. Even if it's impossible to prove everything in a logically consistent system without there being any contradictions - that means there's always more to discover and so mathematicians will never run out of a job - haha :).

[@calcuquack1206]

wow

[@rajputzadii-b4e]

show that f (x)=1/x is continuous at 1 DR peyam will get the this question solved plz my humble request

[@drpeyam]

I just did it!

[@amenbellaaj6422]

i didnt understand a single thing