We know that mathematicians care no more for logic than logicians for mathematics. The two eyes of exact science are mathematics and logic: the mathe… - Augustus De Morgan

Although there is no study which presents so simple a beginning as that of geometry, there is none in which difficulties grow more rapidly as we proceed, and what may appear at first rather paradoxical, the more acute the student the more serious will the impediments in the way of his progress appear. This necessarily follows in a science which consists of reasoning from the very commencement, for it is evident that every student will feel a claim to have his objections answered, not by authority, but by argument, and that the intelligent student will perceive more readily than another the force of an objection and the obscurity arising from an unexplained difficulty, as the greater is the ordinary light the more will occasional darkness be felt. To remove some of these difficulties is the principal object of this Treatise.

The following is exactly what we mean by a <small>LIMIT</small>. ...let the several values of x... bea₁ a₂ a₃ a₄. . . . &c.then if by passing from a₁ to a₂, from a₂ to a₃, &c., we continually approach to a certain quantity l [lower case L, for "limit"], so that each of the set differs from l by less than its predecessors; and if, in addition to this, the approach to l is of such a kind, that name any quantity we may, however small, namely z, we shall at last come to a series beginning, say with a_n, and continuing ad infinitum,a_n a_n+1 a_n+2. . . . &c.all the terms of which severally differ from l by less than z: then l is called the limit of x with respect to the supposition in question.

The manner in which a paradoxer will show himself, as to sense or nonsense, will not depend upon what he maintains, but upon whether he has or has not made a sufficient knowledge of what has been done by others, especially as to the mode of doing it, a preliminary to inventing knowledge for himself.