"There is a ... such that for each ... there is a ...". Epsilon and h are going to zero, much as they would in limits, so why isn't there a quick shorthand as we use with limits? I had assumed I could use the limit notation, since, after all, that's *essentially* what I was doing anyway. I specified I was approaching 0+, and hence indicating that h is, for the purpose of the limit, a positive number that was "approaching" zero, and could get arbitrarily small, and in fact must get arbitrarily small for rest of the maths to hold. I don't quite see why this isn't essentially what a limit is. A limit as h goes to 0 doesn't find the value at 0, it's the value of convergence of values of h that get arbitrarily close to 0. No?
Edit: That's not to say that I object to your suggested notation, and in fact I can see some benefits as far as clearing up any possible confusion. I'm just wondering if it's really necessary, or if it's more of a consideration for others?
Edit: That's not to say that I object to your suggested notation, and in fact I can see some benefits as far as clearing up any possible confusion. I'm just wondering if it's really necessary, or if it's more of a consideration for others?
~ Jay Daniel Fox