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Integers {....-3,-2,-1,0,1,2,3.......} - Coggle Diagram
Integers {....-3,-2,-1,0,1,2,3.......}
Positive Integers
Smallest - 1
Greatest - not defined
Have a + sign before them
Lie to the right of zero
Are always greater than 0 and negative integers
Ascending order = 1,2,3,4,5,6,7,8,9,10.....
Descending order - .........,10,9,8,7,6,5,4,3,2,1
Can be represented on a number line.
Negative Integers
Greatest : (-1)
Smallest : not defined
Have a (-) before them
Lie on the left of zero
Are always smaller than 0 and positive integers
Ascending order : .....-10,-9,-8,-7,-6,-5,-4,-3,-2,-1
Descending Order : -1,-2,-3,-4,-5,-6,-7,-8,-9,-10
Can be represented on a number line.
Neutral Integers
0 is the only neutral integer.
We never write it as +0 or -0.
It does not make sense either.
Addition
When two integers have the same sign, add them and put the common sign.
When they have different signs, add them and put the sign of the absolute value before the answer.
Subtraction
When two numbers are subtracted, add the additive inverse of the second number.
Additive Inverse - The numbers which when added together result in 0 are called additive inverse of each other. They are also the positive (+ve) and negative (-ve) values of a number.
Eg : +3 and -3, +8 and -8, are additive inverses.
Additive identity - 0 is the additive identity of the integers as when 0 is added to any number, the result is the number itself.
Successor - The (number+1) is the successor of the number.
Eg : -1's successor is 0
3 successor is 4
-3 successor is -2.
Predecessor - The (number-1) is the predecessor of a number.
Eg ; 7 predecessor is 6
-8 predecessor is -9
For addition
x+(+y) = x + y
x+(-y) = [x-y]
-x+y => 1. subtract the smaller one from the bigger one 2. put the sign of the greater integer.
Eg : -2+5 => 5-2=3 => |5| > |2| => +3
2+(-5) = 2-5 = -3
-5+3 => 5-3 = 2 => |5| > |3| => -2
2+(+5) = 2 + 5 = 7
For subtraction -
-x-y => x+y => put the - sign
-x-(-y) = -x+y = same rules as addition.
+x-y = x - y
-6-1= - 7, -10-1 = - 11
Eg : 5-3 = 2 , 3-5 = -2 , 8-5 = 3
-6-(-7) = -6+7 = 1 , -10-(-8) = -10=8 = -2
Absolute value = The value of an integer regardless its sign. the modulus of a positive number is simply the number. The modulus of a negative number can be found by multiplying it by −1 or ignoring its negative sign. The signs / symbols |x| is known as mod or modulus . It is read as "mod x" . Eg : |2|=2 , |-6| = 6 , |-18| = 18 , |0|=0 , |-1| = 1