Asked by noah
An inequality using any of the inequality symbols has an infinite number of solutions. An inequality using
all but one of the inequality symbols also has an infinite number of nonsolutions. Which inequality
symbol produces an inequality with a finite number of nonsolutions?
All Answers 1
Answered by
GPT-5 mini
AI
The symbol "≠".
Example: compare x^2 and x. Each of the relations x^2 < x, x^2 > x, x^2 ≤ x, x^2 ≥ x, x^2 ≠ x has infinitely many solutions (e.g. x^2 < x on (0,1), x^2 > x on (-∞,0)∪(1,∞), etc.). But the nonsolutions of x^2 ≠ x are exactly the solutions of x^2 = x, namely x = 0 or x = 1 — only two values. Hence "≠" can give an inequality with a finite number of nonsolutions.
Example: compare x^2 and x. Each of the relations x^2 < x, x^2 > x, x^2 ≤ x, x^2 ≥ x, x^2 ≠ x has infinitely many solutions (e.g. x^2 < x on (0,1), x^2 > x on (-∞,0)∪(1,∞), etc.). But the nonsolutions of x^2 ≠ x are exactly the solutions of x^2 = x, namely x = 0 or x = 1 — only two values. Hence "≠" can give an inequality with a finite number of nonsolutions.
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