## Numbers

*Defendit numerus: There is safety in numbers*

We begin by talking about numbers. This may seen rather elementary but is doesset the scene and introduce a lot of notation. In addition much of what follows isimportant in computing.

### Integers

I will assume you are familiar with the integers.

1,2,3,4,. . .,101,102, . . . , n, . . . , 2^32582657 − 1, . . .

sometime called the whole numbers. These are just the numbers we use for count-ing. To these integers we add the zero, 0, defined as:

*0 + any integer n = 0 + n = n + 0 = n*

Once we have the integers and zero mathematicians create negative integers bydefining (−n) as:

the number which when added to n gives zero, so n + (−n) = (−n) + n = 0.

Eventually we get fed up with writing n+(−n) = 0 and write this as n−n = 0.We have now got the positive and negative integers {. . . , −3, −2, −1, 0, 1, 2, 3, 4, . . .}

You are probably used to arithmetic with integers which follows simple rules.To be on the safe side we itemize them, so for integers a and b

1. a + b = b + a

2. a × b = b × a or ab = ba

3. −a × b = −ab

4. (−a) × (−b) = ab

5. To save space we write a k as a shorthand for a multiplied by itself k times.So 3^4 = 3 × 3 × 3 × 3 and 2^10 = 1024.

Note a^n × a^m = a^(n+m)6. Do note that n^0 =1.

Peace out

@suhaibbinyounis

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