If a set of six numbers, including both rational and irrational numbers, is graphed on a number line, what is the fewest number of distinct points that need to be graphed?

If there are no duplicates among the rational numbers and no duplicates among the irrational numbers, then there must be exactly 6 points.
None of the rational numbers can also be irrational, and none of the irrational numbers can also be rational.

Answered by AL2006 | 2024-06-10

A set of six numbers can be graphed with a minimum of 2 distinct points if there are duplicates among the numbers. If all numbers are unique, then you would need a maximum of 6 distinct points. The exact number depends on duplicates among the rational and irrational numbers.
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Answered by AL2006 | 2024-12-26