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 .

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