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What operations is not closed for polynomials?
division
The natural numbers are closed under division?
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
Is 1 a set closed under division?
yes
Is division closed real numbers?
Yes, but only when the denominator is non-zero. Division by 0 is not defined.
Are rational numbers are closed under addition subtraction division or multiplication?
The set of rational numbers is closed under all 4 basic operations.
What is a counterexample to show that the repeating decimals are closed under addition false?
There cannot be a counterexample since the assertion is true. This requires you to accept the true fact that the terminating decimal 1.25, for example, is equivalent to the repeating decimal 1.25000... (or even 1.24999.... ).
The terminating decimals are closed under division?
no
What is a counterexample to show that the repeating decimals are closed under subtraction false?
In fact, the statement is true. Consequently, there is not a proper counterexample. The fallacy is in asserting that a terminating decimal is not a repeating decimal. First, there is the trivial argument that any terminating decimal can be written with a repeating string of trailing zeros. But, Cantor or Dedekind (I can't remember which) proved that any terminating decimal can also be expressed as a repeating decimal. For example, 2.35 can be written as 2.3499... Or 150,000 as 149,999.99... Thus, a terminating decimal becomes a recurring decimal. As a consequence, all real numbers can be expressed as infinite decimals. And that proves closure under addition.
Give ten examples of natural number are closed under subtraction and division?
You can give hundreds of examples, but a single counterexample shows that natural numbers are NOT closed under subtraction or division. For example, 1 - 2 is NOT a natural number, and 1 / 2 is NOT a natural number.
What is an example of a counterexample for the difference of two whole numbers is a whole number?
There is no counterexample because the set of whole numbers is closed under addition (and subtraction).
Are terminating decimals closed under division?
no, but is a hard question 4 some 1 like me who is young....... thanks 4 asking! (:
What is an counterexample of the set of negative integers is closed under the operation of taking the absolute value?
-3 is a negative integer. The absolute value of -3 is +3 which is not a negative integer. So the set is not closed.
What is a counterexample for the rational numbers are closed under the operation of taking a square root?
2 = 2/1 is rational. Sqrt(2) is not rational.
What is a counterexample to the set of negative numbers is closed under subtraction?
-2 - (-5) = -2 + +5 = +3. (+3 is not in the set of negative numbers.)
Are rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
Are rational numbers closed under division multiplication addition or subtraction?
Rational numbers are closed under addition, subtraction, multiplication. They are not closed under division, since you can't divide by zero. However, rational numbers excluding the zero are closed under division.
What operations is not closed for polynomials?
division
