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Zero divisors: continuous functions over R

  1. Nov 25, 2007 #1
    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?
     
  2. jcsd
  3. Nov 25, 2007 #2
    you should be able to define two nonzero continuous functions whose product is zero function...
     
  4. Nov 25, 2007 #3
    Wow, yea probably. I want to find easy ones. Give me until tomorrow. I'm dead tired. Thanks
     
  5. Nov 25, 2007 #4

    Office_Shredder

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    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
     
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