Math and Arithmetic

# What does it mean to say that integers are closed under addition?

Any time you add integers, the sum will be another integer.

🙏
0
🤨
0
😮
0
😂
0

## Related Questions

If you mean the set of non-negative integers ("whole numbers" is a bit ambiguous in this sense), it is closed under addition and multiplication. If you mean "integers", the set is closed under addition, subtraction, multiplication.

You don't say that "an integer is closed". It is the SET of integers which is closed UNDER A SPECIFIC OPERATION. For example, the SET of integers is closed under the operations of addition and multiplication. That means that an addition of two members of the set (two integers in this case) will again give you a member of the set (an integer in this case).

It means that given a set, if x and y are any members of the set then x+y is also a member of the set. For example, positive integers are closed under addition, but they are not closed under subtraction, since 5 and 8 are members of the set of positive integers but 5 - 8 = -3 is not a positive integer.

A set is closed under a particular operation (like division, addition, subtraction, etc) if whenever two elements of the set are combined by the operation, the answer is always an element of the original set. Examples: I) The positive integers are closed under addition, because adding any two positive integers gives another positive integer. II) The integers are notclosed under division, because it is not true that an integer divided by an integer is an integer (as in the case of 1 divided by 5, for example). In this case, the answer depends on the definition of "whole numbers". If this term is taken to mean positive whole numbers (1, 2, 3, ...), then the answer is no, they are not closed under subtraction, because it is possible to subtract two positive whole numbers and get an answer that is not a positive whole number (as in the case of 1 - 10 = -9, which is not a positive whole number)

Different sets of numbers have different properties. For example,The set of counting numbers is closed under addition but not under subtraction.The set of integers is closed under addition, subtraction and multiplication but not under division.Rational numbers are closed under all four basic operations of arithmetic, but not for square roots.A set S is "closed" with respect to operation # if whenever x and y are any two elements of S, then x#y is also in S. y = 0 is excluded for division.So, the answer depends on what you mean by "number".

It means whatever members of the set you subtract, the answer will still be a member of the set. For example, the set of positive integers is not closed under subtraction, since 3 - 8 = -5

Unfortunately, the term "whole numbers" is somewhat ambiguous - it means different things to different people. If you mean "integers", yes, it is closed. If you mean "positive integers" or "non-negative integers", no, it isn't.

Yes, the whole numbers are closed with respect to addition and multiplication (but not division).The term "whole numbers" is not always consistently defined, but is usually taken to mean either the positive integers or the non-negative integers (the positive integers and zero). In either of these cases, it also isn't closed with respect to subtraction. Some authors treat it as a synonym for "integers", in which case it is closed with respect to subtraction (but still not with respect to division).

Went under is used to mean they have failed, as in drowning. A business that went under is one that has closed or gone bankrupt.

It means that you can do any of those operations, and again get a number from the set - in this case, a polynomial. Note that if you divide a polynomial by another polynomial, you will NOT always get a polynomial, so the set of polynomials is not closed under division.

If you mean integers, well if you have two integers of the same sign that you are adding, add and the sign stays the same. If you have different signs, subtract and keep the sign of the one that has more. Regular numbers you just add them.

It means nothing, really. The distributive property is a property of multiplication over addition or subtraction. It has little, if anything, to do with integers.

The answer depends on which binary operation you mean when you say "combining". Addition, subtraction, multiplication, division, exponentiation, etc.

Add the integers together, then divide it by the number of integers there are, (in this case 5)

Subtraction means addition of the additive inverse. For two numbers a and b, we say a-b when we mean a + (-b) where -b is a number with the property that b + -b = 0. This applies to all real numbers, which of course includes integers.

Positive and negative integers are opposite each other.

Integers form a subset of numbers but I'm not sure if that's what you mean.

negative integers mean the stock price lost that amount. that is why you will also see thenegative integers in the color red.

The set of positive whole numbers is not closed under subtraction! In order for a set of numbers to be closed under some operation would mean that if you take any two elements of that set and use the operation the resulting "answer" would also be in the original set.26 is a positive whole number.40 is a positive whole number.However 26-40 = -14 which is clearly not a positive whole number. So positive whole numbers are not closed under subtraction.

In Set Theory: a set is closed under an operation if performance of that operation on members of the set always produces a member of the same set.In Topology: a closed set is a set which contains all its limit points.

what do this mean? closed statistically in a divorce case

###### AlgebraMath and ArithmeticIdioms, Cliches, and SlangCivil LawsuitsNumbers HighwaysStock MarketChild Support Copyright © 2021 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.