Let x, y be elements ofR such that x not= y. Prove that there exists epsom > 0 such that y not element of[x − epsom, x + epsom]
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Originally Posted by amm345 Let x, y be elements ofR such that x not= y. Prove that there exists epsom > 0 such that y not element of[x − epsom, x + epsom] Since , distance between x and y, denoted Define The distance function is never negative so epsilon is greater than 0 Then.... can you finish it from here?
I'm not sure, I had kinda had that based on the lecture notes he posts online, but I'm still not sure what to do next.
Originally Posted by artvandalay11 Since , distance between x and y, denoted Define The distance function is never negative so epsilon is greater than 0 Then.... can you finish it from here? Assume Then So On the real line, so So and Multiplying by -2 and 2 respectively yields and These two facts imply x=y, but that is a contradiction with the given information
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