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→Limit of a Function: Minor tweak. It will need much more, I'm sure/
Stated precisely, given any tolerance ε (by tradition, the letter ε is always used) x being sufficiently close to 0 will get f(x) within ε of 1. That condition is formally written:
Stated precisely, given any tolerance ε (by tradition, the letter ε is always used) x being sufficiently close to 0 will get f(x) within ε of 1. That condition is formally written:
:<math>|f(x)-1| < \varepsilon</math>
:<math>|f(x)-1| < \varepsilon</math>
In this example, when ε is one quadrillionth, <math>x < 10^{-17}</math> satisfies the condition.
"x is sufficiently close to zero" is formalized as
"x is sufficiently close to zero" is formalized as
:"There is a number δ (by tradition it's always δ) such that, whenever x is within δ of 0, f(x) is within ε of 1".
:"There is a number δ (by tradition it's always δ) such that, whenever x is within δ of 0, f(x) is within ε of 1".