MatemÁtica Conjuntos NumÉricos

The statement is true because a natural number is defined as a positive whole number, starting from 1 and going to infinity. Since an integer is also a whole number, it includes the natural numbers as a subset. Therefore, every natural number is also an integer.

This statement is true because any negative number is smaller than any positive number. For example, -1 is smaller than 1, -2 is smaller than 2, and so on. This is a fundamental concept in mathematics where numbers on the negative side of the number line are smaller than numbers on the positive side.

A letra Q representa o conjunto dos números racionais. Os números racionais são aqueles que podem ser expressos como uma fração, ou seja, uma divisão entre dois números inteiros. Isso inclui números inteiros, números decimais finitos e números decimais periódicos. Portanto, a resposta correta é Racionais.

A letra Z representa o conjunto dos números inteiros.

The correct answer is "Os racionais" because this set includes all the numbers that can be expressed as integers, decimals, fractions, and repeating decimals. Irracionais (irrational numbers) are not included in this set because they cannot be expressed as fractions or repeating decimals. Reais (real numbers) include both rational and irrational numbers, so it is a broader set. Irreais (irreal numbers) is not a recognized mathematical term.

The correct answer is "São os inteiros e positivos, incluindo o zero." This answer states that the natural numbers include both positive integers and zero. It is a commonly accepted definition in mathematics that the set of natural numbers starts from zero and includes all positive integers.

The statement "O número zero é racional" translates to "The number zero is rational" in English. In mathematics, a rational number is defined as any number that can be expressed as a fraction, where both the numerator and denominator are integers. Since zero can be expressed as 0/1, it satisfies this definition and is considered a rational number. Therefore, the correct answer is true.

A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers. However, not all rational numbers are integers. Integers are whole numbers, both positive and negative, including zero. Therefore, not all rational numbers are integers, making the statement false.

The correct answer states that every natural number is an integer. This is true because the set of natural numbers includes all positive whole numbers (1, 2, 3, etc.) and zero, and all of these numbers can be represented as integers without any fractional or decimal parts. Therefore, every natural number can also be classified as an integer.

The statement is false because a positive integer does not have negative divisors. Divisors are numbers that divide evenly into another number without leaving a remainder. Since negative numbers cannot be divided evenly into a positive integer, they cannot be considered as divisors. Therefore, the statement is incorrect.

The given statement is false. The set of non-positive integers includes all the negative integers and zero. However, the given set includes the positive integer 0, which means it is not a set of non-positive integers.

The correct answer states that every whole number is a natural number, and every fractional number is a rational number. This is true because the set of natural numbers includes all positive whole numbers, and the set of rational numbers includes all numbers that can be expressed as a fraction. Therefore, the statement "TODO NÚMERO INTEIRO É NATURAL, TODO NÚMERO FRACIONÁRIO É RACIONAL" is correct.