Notes on Finite and Infinite Sets

Introduction

• Discusses the concepts of finite and infinite sets.
• Finite: A set that does not go on forever.
• Infinite: A set that goes on forever.

Definitions

• Whole Numbers: 0, 1, 2, 3, 4, 5, ... (an infinite set).
• Finite Set: A set with a number of elements that is a whole number.
• Infinite Set: A set with no particular whole number that describes the number of elements.

Examples of Sets

Set A: {2, 4, 6}

• Contains 3 elements.
• Cardinality: 3 (a whole number).
• Conclusion: Finite set.

Set B: Empty Set (∅)

• Contains 0 elements.
• Cardinality: 0.
• Conclusion: Finite set (0 is a whole number).

Set C: {2, 4, 6, 8, 10}

• Elements are increasing by 2.
• Contains 5 elements.
• Cardinality: 5 (a whole number).
• Conclusion: Finite set.

Set D: {2, 4, 6, ...}

• Elements increase without end (continues infinitely).
• Conclusion: Infinite set (no largest element, no whole number to count elements).

Homework Example

• Set of all X such that X is a natural number greater than 60.
• Natural numbers: 1, 2, 3, ... (also infinite).
• This set starts at 61 and goes on forever (61, 62, 63, ...).
• Conclusion: Infinite set (reason: number of elements is not a whole number).

Conclusion

• Understanding finite and infinite sets is crucial in mathematics.
• Encouragement to like and subscribe for more math content.