# Question about limits and inequalities

1. Nov 14, 2009

### AxiomOfChoice

If you have

$$T < M + \epsilon,$$

where $\epsilon > 0$ is arbitrary, does this imply

$$T \leq M?$$

2. Nov 14, 2009

### VeeEight

Yes.

3. Nov 15, 2009

### Office_Shredder

Staff Emeritus
Suppose it wasn't. Let epsilon be T-M (which is positive). What do you conclude?