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Define f:R→R as follows:

f(x)= x- ⌊x⌋ if ⌊x⌋ is even.

f(x)= x- ⌊x+1⌋ if ⌊x⌋ is odd.

Determine those points where f has a limit and justify your conclusions (using δ and ε).

2. Relevant equations

3.

The attempt at a solution involved a graph of the situations of f(x). With this graph my group and I determined f(x) has a limit at x_0 iff x_0 is not an odd integer. However, we hare having a hard time proving it, and, although the graph says we are right, we must use δ and ε in a formal proof.

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# Homework Help: Proving f(x) has a limit at all points not odd

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