Is the set of whole numbers closed under addition? Subtraction?
Division? Mulitiplication?
Is the set of integers closed under addition? Subtraction?
Division? Mulitiplication?
Is the set of rational numbers closed under addition? Subtraction?
Division? Mulitiplication?
I don't even know what the question is can someone please help? I don't even know what a rational number or a interger is and what is a whole number?
2006-09-04 12:07:37 · 12 answers · asked by Anonymous in Education & Reference ➔ Homework Help
THat is why I don't get it there is no set of numbers on the paper.
2006-09-04 12:15:20 · update #1
the set of whole numbers is closed under addition (2 +2 is still a whole number), and multiplication (2x3 is still whole) but not under subtraction (2-4 becomes negative, not a whole number) and division (2 / 3 is not whole, nor is 6 divided by 7).
integers are closed under addition, subtraction and multiplication. division is not counted, as 5 divided by -6 gives a non-integer.
rational numbers are closed under all operations.
a whole number is all positive numbers that have no decimal points or fractions, including zero. for example: 0,1,2,3,4,5,6...
integers are like whole numbers, except they include negative numbers. they also have no decimal points: -5,-4,-3,-2,-1,0,1,2,3
rational numbers are numbers which can be expressed in fraction. thus, six is rational because it can be expressed as 12/2, 0.6666... is also rational because it can be expressed as 2/3. pi (3.1416...) is not rational, nor are irregular square roots (square root of two, or square root of five).
when you say a set is closed under addition, it means that if you add any element of the set, it will still belong to the same set. for example, integers are closed under addition, because no matter what number you add, you'll still end up with an integer. the same goes for subtraction, multiplication and division.
2006-09-04 12:18:53 · answer #1 · answered by lemons 3 · 0⤊ 0⤋
Is the set of Whole numbers closed under addition? The set of whole numbers is all counting (natural ) numbers Plus Zero So if you add any two of these will you always get a Whole number The set is closed for addition YES (But For subtraction) 10 - 25 = -15 You do not get a whole number so the set does not always provide an answer so the set is not closed for subtraction . Division 2/5 = .4 not a whole number not closed Multiplication yes closed. Rational number is a fraction ( Ratio ) Integer is all whole numbers and their Opposite ( example 3 and -3 are opposites of each other).
is This any help?
2006-09-04 12:42:00 · answer #2 · answered by John M 1 · 0⤊ 0⤋
A set is said to be closed under an operation if when you apply the operation to two members of a set, you always get another member of that set.
Whole numbers are closed under all operations except division, because dividing one whole number by another can sometimes result in a non-whole number. Same for integers.
Rational numbers are closed under all operations..
A rational number is a number that can be expressed as a ratio of two whole numbers.
An integer and a whole number are the same thing - a number without a fractional part. So 2 is an integer, but 2.3 is not. 2.3 is a rational number because it can be expressed as the ratio of two whole numbers, namely 23 and 10.
2006-09-04 12:24:28 · answer #3 · answered by Anonymous · 0⤊ 0⤋
1. Closed under add. and mult. Not closed under subtraction, b/c you can get a negative number for an answer. Not closed under division b/c you can get a fraction answer or undefined.
2. Closed under all but div. same reason as 1.
3. Yes for all.
Whole numbers: 0, 1, 2, 3.....
Integers: ...-2, -1, 0, 1, 2...
Rational numbers include integers and ratios of integers (fractions).
Closed means that the answer to a problem is the same type of number as the ones you started with (in the same set, such as whole numbers).
2006-09-04 12:18:56 · answer #4 · answered by Speedy 3 · 0⤊ 0⤋
You're talking about a set of whole numbers, integers, rational numbers, etc......But you didn't show them in your question. So, in order to tell whether they are under addition, subtraction, division or multiplication, we have to see the set of numbers.
2006-09-04 12:11:37 · answer #5 · answered by Anonymous · 0⤊ 0⤋
1.whole numbers closed under addition and multiplication
2.set of integers closed under addition and multiplication
3.rational numbers closed under both addition and subtraction division and multiplication
closure property:when you add two natural numbers you get a natural number as the sum (closed)
when you subtract one natural no from another it is not necessary that the answer is also a natural number(n0t closed)
2006-09-04 12:17:52 · answer #6 · answered by raj 7 · 0⤊ 0⤋
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2016-12-18 04:55:09 · answer #7 · answered by ? 4 · 0⤊ 0⤋
an integer is a whole number and a rational number is a number which can be square rooted i think
2006-09-04 12:09:48 · answer #8 · answered by transferredmalice 2 · 0⤊ 0⤋
Dont you have a book to study on these subjects? You need to study the problems in order to solve them, as only giving the answers will not give you the knowledge to work it out.
2006-09-04 12:12:28 · answer #9 · answered by zuriel 3 · 0⤊ 0⤋
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2006-09-04 12:16:22 · answer #10 · answered by Anonymous · 0⤊ 0⤋