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### 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

is clear. It becomes more difficult with

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

as we must apply the well known rule

+ + = +

+ – = –

– + = –

– – = +

##### Fractions

What should we think of

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

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 inversef^{ − 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.