A finite set has a limited number of elements, while an infinite set has an unlimited number of elements.
Finite Sets
A finite set is defined as a set with a specific, countable number of elements.
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Example: According to the reference, the set D = {1, 2, 3, 4, 5, 6} is a finite set containing six elements.
Set Number of Elements D = {1, 2, 3, 4, 5, 6} 6 -
Other examples of finite sets include:
- The set of days in a week.
- The set of letters in the English alphabet.
- The set of students in a specific class.
Infinite Sets
An infinite set, on the other hand, has an unlimited number of elements and is not countable. If a set is not finite, then it is infinite.
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Example: The reference states that the set of all points in a plane is an infinite set. This is because there is no limit to how many points can exist in a plane.
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Other examples of infinite sets include:
- The set of all natural numbers (1, 2, 3, ...).
- The set of all real numbers.
- The set of all integers.
In summary, the key difference is that finite sets have a countable number of elements, while infinite sets have an unlimited number. The example set D = {1, 2, 3, 4, 5, 6} has 6 elements (finite) and the points in a plane has no limit (infinite).
