Re: Uniform Continuity Proof

Re: Uniform Continuity Proof

Thanks for this, it did help me with understanding it.

Although I am now wondering how the '+ x' at the end would adjust this proof.

I'm guessing that I would write "y^{3} + y - x^{3} - x",

Which would then simplify to (y-x)(1 + (y^{2} + yx + x^{2})). Correct?

But then when you pick values for x and y you cannot do so without there being a delta left over in your answer (ie., you can show the contradiction as there is a delta left over)

Does this mean that it is, indeed, uniformly continuous?

Or do I need to choose x and y so that y = x + d/(d+3) (d = delta)

This would then cancel the deltas out and give 1 (as it is the multiplicative inverse), which contradicts the statement that |y^{2} + yx + x^{2}| < 1.

Although my problem with this is that I'm not sure if this fits with the previous restrictions that were made on x and y.

Any help here would be great!

Thanks,

Mark