Posts Tagged 'Analysis'

The Popcorn Function

Continuity is not what it seems. In 1875, the German mathematician Carl Johannes Thomae defined a function P(x) with the following extraordinary property:

P(x) is  discontinuous if x is rational

P(x) is continuous if x is irrational.

A graph of this function on the interval (0,1) is shown below. Continue reading ‘The Popcorn Function’

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