Page 148 - 'Blast_Into_Math

Blast into Math! Analatic nummer theora: ants, ghosts and giants

∞ , and a number L .
1. We start with a sequence of numbers {x n } n=1
2. A ghost number > 0 floats by. We call it a ghost number because it can be very very
small; it only needs to be greater than zero, but it can be very close to zero.

Exercise: In which exercise did you prove that there is no smallest positive rational number?

The number > 0 in the definition of limit is like a ghost number, because it can be so small
that it can barely be seen. Like a ghost.

3. The next part of the definition is: there exists N ∈ N . This means that the ghost number
can find a GIANT NUMBER N ∈ N. The number N is a giant number because it could

be very very large. This is because, by the definition of natural numbers, there is no largest
natural number.
4. The ghost number and the giant number work together as a team. First, the giant number
N squashes all the ants (terms) in the sequence from the first one all the way up to the
N th one. Mathematically, this is the statement for all n> N, which means that we are
only looking at the terms (ants) in the sequence from N +1 onwards. The terms in the
sequence from 1 up to N don’t matter anymore, because they have been squashed!

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