Euler rejected the concept of infinitesimal in its sense as a quantityless than any assignable magnitude and yet unequal to 0, arguing: thatdifferentials must be zeros, and \(\Dy/\Dx\) the quotient \(0/0\).Since for any number \(\alpha\), \(\alpha \cdot 0 = 0\), Eulermaintained that the quotient \(0/0\) could represent any number whatsoever.[23] For Euler qua formalist the calculus was essentially aprocedure for determining the value of the expression \(0/0\) in themanifold situations it arises as the ratio of evanescentincrements.
james stewart essential calculus 2nd edition pdf 447
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