# Newtonian Calculus not rigorous !

Why Newton’s Calculus Not Rigorous?

$f(x ) = \frac {x(x^2+ 5)} { x}$ …[1]

cancel x (≠0)from upper and below => $f(x )=x^2 +5$

$\mathop {\lim }\limits_{x \to 0} f(x) =x^2 +5= L=5$ …[2]

In [1]: we assume x ≠ 0, so cancel upper & lower x
But In [2]: assume x=0 to get L=5
[1] (x ≠ 0) contradicts with [2] (x = 0)

This is the weakness of Newtonian Calculus, made rigorous later by Cauchy’s ε-δ ‘Analysis’.