# Uniform Convergence Issues

**Purpose**

To understand Uniform Convergence Page 183 - Bressound I

> epsilon <- 0.01 > par(mfrow = c(2, 2)) > x <- c(seq(-2, -9e-04, 1e-05), seq(9e-04, 2, 1e-05)) > n1 <- (epsilon/(3 * x * x - x * x * epsilon)) > plot(x, (n1), col = "blue") > plot.new() > x <- c(seq(-2, -0.21, 0.01), seq(0.21, 2, 0.01)) > n1 <- (epsilon/(3 * x * x - x * x * epsilon)) > n2 <- (3 - epsilon)/(epsilon * x * x) > plot(x, (n1), col = "blue") > plot(x, round(n2), col = "blue") |

**As one can see , if you choose a specific small x so that size of first term**

is less than epsilon/3, for the same x you have to choose a much much higher n it basically shoots to infinite.

Lets say at x = 0.1, you choose a specific n that satisfies second piece, that same n will never satisfy the first piece. Basically you cant win the epsilon delta game