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What is a counterexample to show that the repeating decimals are closed under addition false?
Wiki User
∙ 9y ago
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.... ).
Wiki User
∙ 9y ago
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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).
The terminating decimals are closed under division?
no
Is a rational number closed under addition?
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
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 to the set of negative numbers is closed under subtraction?
-2 - (-5) = -2 + +5 = +3. (+3 is not in the set of negative numbers.)
What is the counterexample for the repeating decimals are closed under division?
Division by 0, which can also be written as 0.000... (repeating) is not defined.
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.
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).
The terminating decimals are closed under division?
no
Is a rational number closed under addition?
No. A number cannot be closed under addition: only a set can be closed. The set of rational numbers is closed under addition.
What is closed and not-closed under addition?
The set of even numbers is closed under addition, the set of odd numbers is not.
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.)
When are complex numbers closed under addition?
Quite simply, they are closed under addition. No "when".
Why are odd integers closed under multiplication but not under addition?
The numbers are not closed under addition because whole numbers, even integers, and natural numbers are closed.
ARe odd integers not closed under addition?
That is correct, the set is not closed.
