1. Nov 25, 2007 #1

   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?

    

   teleport, Nov 25, 2007
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3. Nov 25, 2007 #2

   *best&sweetest*

   

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

    

   *best&sweetest*, Nov 25, 2007
4. Nov 25, 2007 #3

   teleport

   

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

    

   teleport, Nov 25, 2007
5. Nov 25, 2007 #4

   Office_Shredder

   

   Staff Emeritus

   Science Advisor

   Gold Member

   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

    

   Office_Shredder, Nov 25, 2007

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