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What binary operations have closure?
Closure depends on the set as much as it depends on the operation.For example, subtraction is closed for all integers but not for natural numbers. Division by a non-zero number is closed for the rational numbers but not integers.The set {1, 2, 3} is not closed under addition.
Why integers need an extension?
In the first stage, the set of all integers needs an extension - to the set of rational numbers - to get closure for division (which is the inverse operation to multiplication).
Is the set of integers closed under subtraction?
yes, because an integer is a positive or negative, rational, whole number. when you subject integers, you still get a positive or negative, rational, whole number, which means that under the closure property of real numbers, the set of integers is closed under subtraction.
Why is rational numbers important?
Extending the set of all integers to included rational numbers give closure under division by non-zero integers. This allows equations such as 2x = 3 to be solved.
What do interger's allow you to do that whole numbers do not?
Integers are closed under subtraction, meaning that any subtraction problem with integers has a solution in the set of integers.
Are the sums and products of whole numbers always whole numbers?
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).
How do we use complex and imaginary numbers?
Among other things, complex numbers play an important role:* In electrical circuits - quantities in AC circuits are described by complex numbers. * In quantum mechanics - the "probability amplitude" is an important concept in quantum mechanics, and it is described by a complex number. * In art - for example, the Mandelbrot set is based on calculations with complex numbers.
What are the numbers in division mutliplication addition subtraction?
You can have counting number in multiplication and addition. All integers are in multiplication, addition and subtraction. All rational numbers are in all four. Real numbers, complex numbers and other larger sets are consistent with the four operations.
What is the difference in subtraction integers and subtracting whole numbers?
None, because the set of integers and the set of whole numbers is the same.
What is an example of subtraction of integers?
Integers are whole numbers as for example 28 minus 17 = 11
How is subtraction and rational numbers are different from adding?
They are different in the same way that subtraction of integers is different from their addition.
What contexts allows negative numbers?
Closure of the set of numbers under subtraction or, equivalently, the existence of additive inverses.
