## Welcome

This blog is for people who think they are no good at maths. I say to you: You are better than you think. Read on for proof.

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Let us start with the simple notion of an expression. As its name suggests, an expression is used to express (or denote) a value. A value may be a sum of money or the weight of an object or the truth of an assertion.

There are two kinds of expressions: constants and variables.

A constant represents a particular value and that value cannot be changed. Examples of constants include $1$, $2007$.

A variable can represent any value (though only one value at time). In addition the value of a variable can be replaced by another expression. We’ll see exactly how to do this later on. We use single italic letters for variables e.g. $X$, $Y$.

All our expressions will denote at most one value, but a value may be denoted by more than one expression. For example the expressions $1+1$ and $2$ both denote the same value.

Now writing

“the expression $X$ denotes the same value as the expression $Y$

over and over would become quite tiresome. So we instead we just write

$X = Y$

pronounced “$X$ equals $Y$“.

Moreover, we may view X = Y not just as a statement of fact but as an expression in its own right. But what, then, is its value?

Exercise – Ask any mathematicians you know what they can tell you about the value of $X = Y$ .