Definitions
Discrete : Different, independents, separate, not of same type |
Discrete Mathematics ( discrete structures ) : Mathematical topic that are different, independents, separate, not of same type |
Integer : whole number without fraction |
Even : even integer |
Odd : odd integer |
At least : same or more (more means bigger by value ) |
At most : same or less ( less means smaller by value ) |
Non-negative: 0 or positive |
Non-positive : 0 or negative |
Increasing sequence : left to right values are always bigger ( same not allowed ) |
Non-decreasing sequence : left to right values are same or bigger |
Decreasing sequence: left to right values are always smaller (same not allowed) |
Non-increasing sequence : left to right values are same or less |
rational number : can be represented by the fraction (ratio) of two integers as p/q, where q is non-zero |
irrational number : is a number that cannot be represented by a ratio of two integers |
Real numbers : include integers, rational and irrational numbers |
Decimal number : the number that we usually see and use (0, 1, 2…9) |
Binary number : number has only two digits, (0 and 1 ) |
Absolute value of a number : is its value without sign |
Equality : is another name of mathematical equation |
Factorial : of a non-negative integer n (written as n!) |
mod (also called modulus) of two integers a mod b is the remainder after a is divided by b |
At least and At most
At least :
example 1: At least 12 ( means 12 or more )
12 , 13 , 13.5 , 1000 etc
example 2 : At least -4
-4 , -3.5 , 0 , 4 etc
At most :
example 1: At most 12 ( means 12 or less )
12 , 11.99 , 10 ,0 ,-1 etc
example 2 : At most -4
-4 , -4.1 , -5 , -10 etc |
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Some warmup preliminaries
Odd, even Integers
Even = 2k
Odd = 2k+1
( for some integer k. k may be even or odd )
0 is even
Note Non-negative and Non-positive
0 is not positive, not negative
Non-negative and at least 0 are same
Non-positive and at most 0 are same |
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Increasing and decreasing
The term increasing usually come with sequence
Numbers
Binary numbers have equivalent decimal values
For example: 00, 01, 10,11 are equivalent to 0, 1, 2, 3
mod
Mod means remainder
even%2 = 0
odd%2 = 1
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