Is the set of all straight lines in the plane whose slope and y-intercept are integers countable?

schlichs6d

schlichs6d

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2022-08-16

Is the set of all straight lines in the plane whose slope and y-intercept are integers countable?

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Kaitlynn Church

Kaitlynn Church

Beginner2022-08-17Added 19 answers

Any line with integer slope and y-intercept corresponds to a pair of integers. Thus, there is an invertible map from the set of all these lines and Z × Z . Cartesian product of two countable sets are also countable. Hence this set of lines is countable.
Crancichhb

Crancichhb

Beginner2022-08-18Added 2 answers

Remember the a line in the plane is completely determined by its slope and a point. If you insist on having both integers then there are no more than Z × Z , which is equipotent with N .

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