Math and Arithmetic

# How do you do addition integers?

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## Related Questions  negetive integers are not closed under addition but positive integers are. Addition and multiplication are operations on integers that are commutative.  Yes it is : a + b = b + a for all integers a and b. In fact , if an operation is called addition you can bet that it is commutative. It would be perverse to call an non-commutative operation addition. Add two positive integers and you ALWAYS have a positive integers. The positive integers are closed under addition.  The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed. The set of integers is closed with respect to multiplication and with respect to addition. The set of integers is closed under addition so that if x and y are integers, then x + y is an integer.Addition of integers is commutative, that is x + y = y + xAddition of integers is associative, that is (x + y) + z = x + (y + z) and so, without ambiguity, either can be written as x + y + z.The same three rules apply to addition of rational numbers. The set of integers is closed under addition so that if x and y are integers, then x + y is an integer.Addition of integers is commutative, that is x + y = y + xAddition of integers is associative, that is (x + y) + z = x + (y + z) and so, without ambiguity, either can be written as x + y + z.The same three rules apply to addition of rational numbers. The rules for addition are as follows:The sum of two negative integers is a negative integerThe sum of two positive integers is a positive integerThe rules for subtraction are as follows:If they are two positive numbers, do it normallyIf there is a negative and a positive ,change it to addition and switch the SECOND integer sign Any time you add integers, the sum will be another integer.  Is the set of negative interferes a group under addition? Explain,   Multiplication is the same as repeated addition. For example 12 * 3 = 12 + 12 + 12 12 * 4 = 12 + 12 + 12 + 12 and so on. 0 belongs to the reals. It is a member of the irrationals, the rationals. It is also a member of the integers; It is a member (the identity) of the group of even integers, 3*integers, 4*integers etc with respect to addition. Subtraction of integers is essentially addition of integers except the second integer is inverted. For example: 5 + 3 = 8 is a simple addition of integers. 5 - 3 = 5 is a simple subtraction of integers. It can be expressed by inverting the second value (the one right after the subration sign) and then switching the subtraction sign to an addition sign. So it would look like: 5 + (-3) = 5. Note that (-3) is the opposite of 3. So to do a more confusing subtraction problem like: 55 - (-5), we could rewrite this as: 55 + -(-5). From here it's easy to see that the two negatives cancel out. 55 + 5 = 60. There is no law of closure. Closure is a property that some sets have with respect to a binary operation. For example, consider the set of even integers and the operation of addition. If you take any two members of the set (that is any two even integers), then their sum is also an even integer. This implies that the set of even integers is closed with respect to addition. But the set of odd integers is not closed with respect to addition since the sum of two odd integers is not odd. Neither set is closed with respect to division. In order to be a group with respect to addition, the integers must satisfy the following axioms: 1) Closure under addition 2) Associativity of addition 3) Contains the additive identity 4) Contains the additive inverses 1) The integers are closed under addition since the sum of any two integers is an integer. 2) The integers are associative with respect to addition since (a+b)+c = a+(b+c) for any integers a, b, and c. 3) The integer 0 is the additive identity since z+0 = 0+z = z for any integer z. 4) Each integer n has an additive inverse, namely -n since n+(-n) = -n+n = 0. They are whole numbers used in division, multiplication, addition and subtraction.  ###### Math and ArithmeticNumbers Copyright © 2020 Multiply Media, LLC. All Rights Reserved. The material on this site can not be reproduced, distributed, transmitted, cached or otherwise used, except with prior written permission of Multiply.