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Full Idea
The problem with infinitesimals is that in some places they behaved like real numbers close to zero but in other places they behaved like zero.
Gist of Idea
Infinitesimals were sometimes zero, and sometimes close to zero
Source
Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 7.1.2)
Book Ref
Colyvan,Mark: 'An Introduction to the Philosophy of Mathematics' [CUP 2012], p.121
A Reaction
Colyvan gives an example, of differentiating a polynomial.
22930 | Lengths do not contain infinite parts; parts are created by acts of division [Aristotle, by Le Poidevin] |
18833 | A continuous line cannot be composed of indivisible points [Aristotle] |
19375 | The continuum is not divided like sand, but folded like paper [Leibniz, by Arthur,R] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
8669 | Between any two rational numbers there is an infinite number of rational numbers [Friend] |
17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |