Zero divisors: continuous functions over R

[teleport]

Does the ring of continuous functions over the real numbers have no zero divisors? If no 0 divisor, how can I prove it? Else, what is a counter example?

 

[*best&sweetest*]

you should be able to define two nonzero continuous functions whose product is zero function...

 

[teleport]

Wow, yea probably. I want to find easy ones. Give me until tomorrow. I'm dead tired. Thanks

 

[Office_Shredder]

Keep in mind if a function is defined piecewise such that each piece is continuous, and all the endpoints match up, you've defined a new continuous function