Infinity

Infinity, in mathematics (represented by the sign oo ), is a most difficult conception, and if used carelessly is liable to lead to fallacies. Numerically infinity signifies not one number but any number too great to be appreciated directly or indirectly by any means at our disposal, liabzzziac, it is usual to infer that b = c, but this is not the case if a =oo; for, so far as our senses can distinguish, there is no difference between different multiples of infinity. Similarly, in geometry, an infinitely distant point means such a one as cannot be compared in position with any point in finite space. Two lines are called parallel when they are in the same plane, and when no amount of continuation of the lines will bring them together. Yet if they actually met at an infinitely distant point, they would still be parallel through the range of finite space. A circle of infinitely large radius would coincide with a straight line, from which the idea springs that if we could travel along a straight line sufficiently far we should return to the starting point.