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I'm new to calculus and I'm teaching myself so please be kind to me :)

How do you prove that f(x) = x is continuous at all points? I know a little bit about deltas and epsilons. I know that for a positive epsilon it is possible to get a delta such that

|(fx) - L| < epsilon for all x that satisfy 0 < |x-a| < delta

but i don't know if that can be applied here

I know that for f(x) = x then if it is continuous then you have to prove

lim (x->a) (fx) = f(a) for all x (i know the definition is more precise)

You can rewrite

lim (x->a) (fx) = f(a)

as

lim (x->a) x= a

but this makes sense intuitively but is it a proof? How could you show this with deltas and epsilons.

I hope this isn't asking too much as I don't think its a hard answer for someone who knows what they are talking about

thanks