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## Homework Statement

show that the function

F:

**C**[tex]\rightarrow[/tex]

**C**

z [tex]\rightarrow[/tex] z+|z|

is continuous for every z

_{0}[tex]\in[/tex]

**C**

**2. Proof**

F is continuous at every z

_{0}[tex]\in[/tex]

**C**if given an \epsilon > 0 , there exists a [tex]\delta[/tex] > 0 such that [tex]\forall[/tex] z

_{0}[tex]\in[/tex]

**C**, |z-z

_{0}|< [tex]\delta[/tex] implies |F(z)-F(z

_{0})|< [tex]\epsilon[/tex].

I know basically how to do this, if someone could just help me with the theoretical steps. First we suppose we are given an epsilon that works? then we have to relate epsilon and delta to find a delta (in terms of epsilon) that works...? then once we have the epsilon and delta we plug back in to verify?

or do i have the concept backwards?