Hello.
I am reading about infinitesimals and came up to the following calculation: (Suppose f is differentiable at point x = a)
[MATH] Δf - dy = Δf -f'(a)Δx = (\frac{Δf}{Δx} - f'(a))\cdot Δx = ε \cdot Δx [/MATH]
Now as Δx approaches 0 the fraction [MATH] \frac{Δf}{Δx}[/MATH] approaches f'(a) and therefore the portion inside the parentheses approaches 0. (Based on the textbook)
But the definition of the fraction [MATH] \frac{Δf}{Δx}[/MATH] as Δx approaches 0 is exactly f'(a).
So why is it that ε approaches 0 instead of ε equals to 0.
Thanks.
I am reading about infinitesimals and came up to the following calculation: (Suppose f is differentiable at point x = a)
[MATH] Δf - dy = Δf -f'(a)Δx = (\frac{Δf}{Δx} - f'(a))\cdot Δx = ε \cdot Δx [/MATH]
Now as Δx approaches 0 the fraction [MATH] \frac{Δf}{Δx}[/MATH] approaches f'(a) and therefore the portion inside the parentheses approaches 0. (Based on the textbook)
But the definition of the fraction [MATH] \frac{Δf}{Δx}[/MATH] as Δx approaches 0 is exactly f'(a).
So why is it that ε approaches 0 instead of ε equals to 0.
Thanks.