Pumping Life

The regular expression is a way to express patterns in a string of letters, like all strings alternating between a and b ("ab", "abab"). The "pumping lemma" means that certain kind of patterns if they describe a long enough string, it must be that it's a repeating pattern. So given a string that fits a pattern, it's possible to lengthen the string to however long you'd like, by repeating a smaller pattern within the larger pattern however many times you'd like.

In our example, the pattern "abab...", you can imagine any arbitrarily long string of letters that fits the pattern. The pumping lemma says that because there HAS to be a repeating sub pattern within the pattern "abab...", we can find an example that fits the pattern, and the example can be as long as we'd like.