Page:Calculus Made Easy.pdf/159

 $$(1+\tfrac{1}{10})^{10}$$ or $$2.593$$ times the original $$1$$. But if only we take n sufficiently large (and the corresponding $$\dfrac{1}{n}$$ sufficiently small), then the final value $$\left(1+\dfrac{1}{n}\right)^n$$ to to which unity will grow will be $$2.71828$$.



Epsilon. To this mysterious number $$2.7182818$$ etc., the mathematicians have assigned as a symbol the Greek letter $$\epsilon$$ (pronounced epsilon). All schoolboys know that the Greek letter $$\pi$$ (called pi) stands for $$3.141592$$ etc.; but how many of them know that epsilon means $$2.71828$$? Yet it is an even more important number than $$\pi$$!

What, then, is epsilon?

Suppose we were to let $$1$$ grow at simple interest till it became $$2$$; then, if at the same nominal rate of interest, and for the same time, we were to let $$1$$ grow at true compound interest, instead of simple, it would grow to the value epsilon.

This process of growing proportionately, at every instant, to the magnitude at that instant, some people