Notation in Mathematical Arguments

Maths: Edexcel A Level Pure Maths, topic 1.2.5

Notation in Mathematical Arguments

When studying maths at a higher level, you need to be able to write mathematical arguments using the correct notation.

Implies

Implies

The implies symbol is a type of arrow written as $\Rightarrow$ .
We use this symbol to show when one equation implies that another equation is true.
For example, $x = 5$ implies that $x^2 = 25$ .
So we can write $x = 5 \Rightarrow x^2=25$
Note that this relationship only goes one way, as $x^2=25$ does not imply that $x=5$ as it could also equal −5.

Equivalence

Equivalence

The double-ended arrow symbol $\Leftrightarrow$ is used to show when two equations are equivalent.
This means that one equation being true implies the other is true, and vice versa.
For example, $x^2 - y^2 = 9 \Leftrightarrow (x+y)(x-y) = 9$

Therefore

Therefore

The symbol for the word 'therefore' is ∴, which is a triangle of three dots.
The symbol does not show a relation between equations, but is used as shorthand instead of writing out the word 'therefore'.
For example, $x = 2a$ , therefore $x$ is even.
So we can write $x = 2a$ ∴ $x$ is even.

Because

Because

The symbol for the word 'because' is ∵, which is an upside-down triangle of three dots.
The symbol does not show a relation between equations, but is used as shorthand instead of writing out the word 'because'.
For example, $x^2 + 1 = 5$ because $x = 2$ .
So we can write ∵ $x=2,\; x^2 +1=5$

Test yourself on Notation in Mathematical Arguments

Which of the following symbols is used as shorthand for the word 'because'?
Which symbol should we use in place of the letter A?

$x= 13$ **A** $x^2 = 169$
Which symbol should we use in place of the letter A?

$x(x+10)=5$ **A** $x^2 +10x = 5$

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