prime number, real number, natural number, whole number, negative number, 等等所有的有关number的概念的包含关系和名词解释

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Welcome to our exploration of number systems. Numbers are classified into different types based on their properties. We have natural numbers starting from one, whole numbers including zero, integers with negative numbers, rational numbers as fractions, and real numbers encompassing all numbers on the number line. This diagram shows how these number sets are nested within each other, with each inner circle being a subset of the outer circles. Natural numbers are the basic counting numbers starting from one. Within natural numbers, we have a special subset called prime numbers. Prime numbers are natural numbers greater than one that have exactly two factors: one and themselves. Examples include two, three, five, seven, and eleven. Numbers that are not prime and greater than one are called composite numbers, like four, six, eight, and nine. The number one is special - it's neither prime nor composite. Integers expand our number system to include negative numbers. The set of integers includes all whole numbers and their negative counterparts, extending infinitely in both directions. Negative numbers are any numbers less than zero and include negative integers like minus one and minus two, negative fractions like minus one half, and negative irrational numbers like minus pi. Zero serves as the boundary between positive and negative numbers, being neither positive nor negative itself. Rational numbers are those that can be expressed as fractions, where both numerator and denominator are integers. This includes all integers, terminating decimals like zero point two five, and repeating decimals like zero point three three three. Irrational numbers cannot be written as fractions and have non-terminating, non-repeating decimal expansions. Famous examples include pi, square root of two, and e. Together, rational and irrational numbers form the complete set of real numbers, filling every point on the number line. To summarize what we have learned: Number systems form a nested hierarchy starting from natural numbers and expanding to real numbers. Prime numbers are special natural numbers with exactly two factors. Integers extend our system to include negative numbers and zero. Rational numbers can be expressed as fractions, while real numbers encompass both rational and irrational numbers, filling the entire number line.