In English, for a thing to be ``equal'' to another is to assert that two different things are in fact the same - a rather oxymoronic thing if one thinks about it. In mathematics it means that two (possibly) different symbols in fact stand for the same thing - a rather more sensible quality.
The simplest statement of equality, one that is always correct for
any possible symbol that stands anything at all is the tautology:
That is, whatever stands for is the same as itself. It is what it is. As a symbol for a number, it has whatever value it has. This law is so fundamental that it is difficult to imagine any sort of logical system where it is not true.
Simple or not, obvious or not, there are (amazingly enough) times we
will want to start with this in a derivation. Again observe that in
algebra the statement:
While we are discussing basic equality, we will add to these fairly
obvious statements the less obvious rule of transitivity. If