Delta Epsilon Proofs

[solemn crane]

Can somebody send me some material to master delta-epsilon proofs for continuity, the material given to us in the lectures are very subpar and I wasn't able to find really good materials online.
Thank you

[fair badge]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with:

+close

3. Feel free to nominate the person for helper of the week in #helper-nominations
4. Do not ping the mods, unless someone is breaking the rules.
5. If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[maiden tapir]

so examples?

try to analyse the thomae function thats a good one

[undone tinsel]

Introduction to Real Analysis by Bartle, tons of exercises and tedium, very sturdy as a reference

[solemn crane]

Yeah i need to learn how to do tricky problems, like with piecewise functions

Thanks i will check it out

[maiden tapir]

rudin has some good exercises too

[solemn crane]

Do these books have solutions?

[maiden tapir]

rudin has as many solution manuals as it has pages!

[solemn crane]

How is the one by Rudin titled?

[undone tinsel]

Iirc solutions to Bartle's odd numbered problems are available

[maiden tapir]

but epsilon delta proofs are not that useful for general functions on R though

[solemn crane]

Thats a requirement for a course lol

[maiden tapir]

for example

[undone tinsel]

Baby Rudin is its nickname, being the first of a series of 3 analysis books

[maiden tapir]

you can technically do it but proving continuity of a polynomial is in itself tedious with just epsilon delta methods

[solemn crane]

Yeah I know, we also use the basic 3 step continuity test and using sequences, but yeah. We also need to know how to do proofs for uniform continuity with utilization of delta epsilon

But bay Rudin looks nice, thx

[maiden tapir]

okay

also as a side note

id like to add that you should read a seperate book on this topic too along with rudin