Mathematics for Computer Scientists






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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