Question

How many solutions does the inequality x > 12 have? Explain.

Answer 1

Infinite solutions

Explanation:

Suppose there are finite solutions to x > 12

Then there exists a largest solution, which we call X

But X + 1 > X, and X > 12, so by transitivity X + 1 > 12 and thus is an even larger solution

this means X is not the largest solution

Therefore, by contradiction, the assumption that there are only finite solutions is false