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What is a counterexample to show that the repeating decimals are closed under subtraction false?
Wiki User
∙ 11y ago
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.
Wiki User
∙ 11y ago
Anonymous
False because they will always repeating
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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.
Which sets of numbers are closed under subtraction?
To be closed under an operation, when that operation is applied to two member of a set then the result must also be a member of the set. Thus the sets ℂ (Complex numbers), ℝ (Real Numbers), ℚ (Rational Numbers) and ℤ (integers) are closed under subtraction. ℤ+ (the positive integers), ℤ- (the negative integers) and ℕ (the natural numbers) are not closed under subtraction as subtraction can lead to a result which is not a member of the set.
Under what operation is the set of positive rational numbers not closed?
Subtraction.
Are rational numbers are closed under addition subtraction multiplication and division?
They are closed under all except that division by zero is not defined.
Why is the set of positive whole numbers closed under subtraction?
The set of positive whole numbers is not closed under subtraction! In order for a set of numbers to be closed under some operation would mean that if you take any two elements of that set and use the operation the resulting "answer" would also be in the original set.26 is a positive whole number.40 is a positive whole number.However 26-40 = -14 which is clearly not a positive whole number. So positive whole numbers are not closed under subtraction.
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 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.... ).
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).
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.)
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.
Is the set of irrational numbers closed under subtraction?
No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction: pi - pi = 0. pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number as well, which it isn't. Therefore the set of irrational numbers is NOT closed under subtraction.
Are polynomial expressions closed under subtraction?
Yes they are closed under multiplication, addition, and subtraction.
Are the prime numbers closed for subtraction?
No.
Are rational numbers closed under subtraction?
Yes. They are closed under addition, subtraction, multiplication. The rational numbers WITHOUT ZERO are closed under division.
Are integers closed under subtraction?
Yes.
Is a counting number closed under subtraction?
No.
What operations are closed for integers?
Addition, subtraction and multiplication.
