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Select any irrational number and turn it into a rational number by using addition subtraction multiplication division or exponentiation?
Other than multiplication by 0 or by its own reciprocal, it if often not possible. Try it with pi, if you think otherwise.
What is the field of mathematics?
In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure which is widely used in algebra, number theory, and many other areas of mathematics.
When is a set of negative irrational numbers closed?
It cannot be closed under the four basic operations (addition, subtraction, multiplication, division) because it is indeed possible to come up with two negative irrational numbers such that their sum/difference/product/quotient is a rational number, indicating that the set is not closed. You will have to think of a different operation.
If a non-terminating decimal that is not a fraction is called irrational what do you call a non-terminating decimal that is a ratio of rational numbers such as 1 over 7?
It is called a rational number. The rational numbers are closed under the operations of addition, subtraction, multiplication, and division (not dividing by 0). The fact that it is not terminating is not important at all. In fact, if we use other bases besides base 10, we will see that the set of numbers that are rational or irrational doesn't change. However, if we use another base, for example base 3, then the number 1/3 in base 3 can be represented with a terminating "decimal" (technically not decimal). The set of rational numbers that have terminating "decimals" depends on the base.
What do rational and irrational numbers have in common?
Rational and irrational numbers are part of the set of real numbers. There are an infinite number of rational numbers and an infinite number of irrational numbers. But rational numbers are countable infinite, while irrational are uncountable. You can search for these terms for more information. Basically, countable means that you could arrange them in such a way as to count each and every one (though you'd never count them all since there is an infinite number of them). I guess another similarity is: the set of rational numbers is closed for addition and subtraction; the set of irrational numbers is closed for addition and subtraction.
