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3 years ago

The cardinality of the set of positive integer is infinity. (True or False)

Mathematics

2 answers:

Bad White [126]3 years ago

8 0

Answer:

It is false, because infinity is not a cardinality. The set N of positive integers is infinite and its cardinality is, if you wish, ℵ0 , the smallest infinite cardinal number, at least in an axiomatic set theory. A set S is infinite if and only if there exists a bijection between S and a proper subset of S , i.e. a subset of S different from S . Now the successor function s:N→N∗ is such a bijection; this follows from Peano’s axioms for arithmetic.

Anestetic [448]3 years ago

7 0

Answer: false

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10. Error Analysis A student draws a triangle with a perimeter 36 cm. The

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Answer:

see the explanation

Step-by-step explanation:

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The <u>Triangle Inequality Theorem</u> states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

In this problem

If the perimeter of triangle is equal to 36 cm

The longest side can't be equal to 18 cm

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Because if the longest side is equal to 18 cm, and the perimeter is equal to 36 cm, then the sum of the other two sides is equal to 18 cm

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3 years ago

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both increased by 2

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Question:

The numerator and denominator of a fraction are in the ratio of 3 to 5. If the numerator and denominator are both decreased by 2, the fraction is now equal to $\frac{1}{2}$ .

If n = the numerator and d = the denominator, which of the following systems of equations could be used to solve the problem?

5n = 3d and n - 2 = 2d - 4

5n = 3d and 2n - 4 = d - 2

3n = 5d and 2n - 4 = d - 2

Answer:

5n = 3d and 2n – 4 = d – 2

Solution:

Let n be the numerator of the fraction and d be the denominator of the fraction.

Given the numerator and denominator of a fraction are in the ratio of 3 to 5.

This can be written as n : d = 3 : 5.

⇒ $\frac{n}{d}= \frac{3}{5}$ – – – – (1)

Do cross multiplication, we get

⇒ 5n = 3d

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⇒ $\frac{n-2}{d-2}= \frac{1}{2}$

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