#### kiriyama

1. Prove if f:R->R is periodic and continuous, then f is uniformly continuous

2. There exists h that does not equal zero such that f(x+h)=f(x)

#### matt grime

Homework Helper
Can you think of any results you know about conditions that make continuous functions into uniformly continuous ones?

#### HallsofIvy

For 1, I agree with matt grime, Think about theorems that say when a continuous function is uniformly continuous (on a given set of course- "uniform" continuity is always defined on a given set. You want to prove that this function is uniformly continuous on the set of all real numbers. Knowing the function is periodic means you can look at a finite interval!)

For 2, exactly what is the DEFINITION of "periodic"?

### The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving