Maeckes logo

<    1      2    >


Minus sign

A minus sign (–) is always immediately associated with subtraction and negative numbers. That is logical, but there is more.

 


Subtraction

The calculation of

5 – 2 = 3

is clear. It becomes more difficult with

2  – 7 = –3

as now a negative number is created. A bit more complicated is

5 – (–2) = 7

as we must apply the well known rule

 + + = + 
 + – = –
 – + = –
 – – = +

 


Fractions

What should we think of

0.5 = 2−1

Here we have no negative values, and yet we use a minus sign. Many people think this is confusing. You could have written a fraction in stead

We see here that numbers with negative exponents are just fractions, for

This is because we work with decimal numbers.

 


Imaginary numbers

For the reciprocal of the imaginary unit you get

i –1 = –i

That is only possible because i has no real value.

 


Inverse functions

The minus sign is also used for inverse functions. The notation is

f (x) with the inverse  f  − 1(x)

On calculators we use

sin-1     for the inverse sine
sinh-1   for the inverse hyperbolic sine

and that is very simple.

 


Additional information

The German mathematician Johannes Widmann (1460 - 1498) has introduced the plus sign and the minus sign.

 


Deutsch   Español   Français   Nederlands