Who is the inventor of the epsilon criteria, which is used on solving limit problems?

Answer 1

There are a few mathematicians who pioneered the epsilon criteria for solving limit problems, and the related epsilon delta criteria for the continuity of functions. Augustin-Louis Cauchy done an incredible amount of work in real and complex analysis and I think that it was he who first used the epsilon criteria, to give a rigorous definition of what it was for something to tend to a limit. However, other mathematicians such as Karl Weierstrass and Bolzono also contributed vastly to the subject.

Answer 2

Weierstrass was the inventor of the epsilon usage in proving limits exist or do not exist. Archimedes did not use epsilon or limits even though he used methods of exhaustion similar to limits used today.

Answer 3

This definition is taken from Calculus (2d version), Salas and Hille Definition of a cut back the cut back of a function f(x) as x methods c is given as L if and provided that --- for each epsilon extra desirable than 0 there exists a delta extra desirable than 0 such that if 0 decrease than relatively the fee of [x -c] decrease than delta, then relatively the fee of [f(x) - L] is decrease than epsilon. sturdy success!

Answer 4

It goes back, theoretically speaking, to the time of so called method of exhaustion that goes back 2300 years or even more. It was conceptually used by Archimedes and was known long before him.
However the use of epsilon belongs to Augustin-Louis Cauchy (1789-1857) used ε in 1821 in Cours d'analyse (Oeuvres II.3).
Curious that the lim. (with a period) was used first by Simon-Antoine-Jean L'Huilier (1750-1840).

Answer 5

It all goes back to the method of exhaustion, which Eudoxus was the founder of.

It's the same with calculus, there is a misconception that Newton & Leibniz invented calculus, when in fact what they did was develop the link between differential and integral calculus.

Earliest forms of integral calculus go back to Eudoxus and his method of exhaustion.

In fact, the whole idea of limits goes back to the method of exhaustion.

Answer 6

dragos,hit the site

http://mathworld.wolfram.com/Limit.html

you might get some more info on this