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Set Theory Symbols and Definitions

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Questions and Answers

What is the symbol '∪' used for?

The symbol '∪' is used to represent the union of sets, which means it includes all elements that are in at least one of the sets.

What does 'N' represent in set theory?

'N' represents the set of natural numbers, which includes all positive whole numbers (1, 2, 3, ...) and zero.

Are all real numbers rational?

No, not all real numbers are rational. Real numbers include both rational numbers (which can be expressed as fractions) and irrational numbers (which cannot be expressed as fractions).

Why are real numbers considered both rational and irrational?

Real numbers are considered both rational and irrational because the set of real numbers includes all rational numbers (which can be expressed as fractions of integers) and all irrational numbers (which cannot be expressed as fractions of integers). Signup and view all the answers

What is the difference between rational and irrational numbers?

Rational numbers can be expressed as fractions of integers, while irrational numbers cannot be expressed as fractions of integers. Signup and view all the answers

What is the difference between integers and natural numbers?

Integers include all whole numbers, both positive and negative, as well as zero. Natural numbers are all positive whole numbers, excluding zero. Signup and view all the answers

Study Notes

Set Theory Notation

The symbol '∪' is used to represent the union of two sets, which combines all elements from both sets into a single set.

Set Theory Basics

'N' represents the set of natural numbers in set theory, which includes all positive integers (1, 2, 3, ...).

Number Classification

Not all real numbers are rational; rational numbers are a subset of real numbers.
Real numbers can be classified into two categories: rational and irrational numbers.

Rational vs. Irrational Numbers

Rational numbers are real numbers that can be expressed as the ratio of two integers (e.g., 3/4 or 22/7).
Irrational numbers are real numbers that cannot be expressed as a simple fraction (e.g., π or the square root of 2).

Integers and Natural Numbers

Integers include all whole numbers, both positive and negative, including zero (..., -3, -2, -1, 0, 1, 2, 3, ...).
Natural numbers, also known as positive integers, are a subset of integers that only include positive whole numbers (1, 2, 3, ...).

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Test your knowledge of set theory symbols and definitions, including elements, subsets, intersections, unions, and different sets of numbers like real, rational, integers, and natural numbers.