3.3 No one

``No one'' is a little different from the other two. It is a negation term. Let's consider an example:

``No one can defeat me!''

This means that there does not exist a peron who ``can defeat me.'' Now, how can we bind a symbol to nobody?

We cannot.

However, we can use the ``there exist'' notation, and combine that with a negation. Here is how to do it in English:

``It is not true that there exist an entity x such that x can defeat me.''

In mathematical symbol, we have the following, assuming $\mathrm{E}$ means all the entities, and $\mathrm{P}(x)$ means ``x can defeat me'':

$\neg(\exists x \in \mathrm{E}: \mathrm{P}(x))$

Note that we can also rearrange things a little, and use the ``for all'' notation instead. In English;

``For all entity x, it is not true that x can defeat me.''

In mathematical symbol, we have:

$\forall x \in \mathrm{E}: \neg \mathrm{P}(x))$