Q: What does and infinite number of solutions?

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This question has an infinite number of solutions !

There are an infinite number of solutions.

it means you can never run out of possible solutions - there are an infinite number of them.

An algebraic equation with an infinite number of solutions

Either an infinite number or none.

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an infinite number of solutions

It depends on the equation. Also, the domain must be such that is supports an infinite number of solutions. A quadratic equation, for example, has no real solution if its discriminant is negative. It cannot have an infinite number of solutions. Many trigonometric equations are periodic and consequently have an infinite number of solutions - provided the domain is also infinite. A function defined as follows: f(x) = 1 if x is real f(x) = 0 if x is not real has no real solutions but an infinite number of solutions in complex numbers.

An infinite solution means that are an infinite number of values that are solutions.

They have an infinite number of solutions.

This question has an infinite number of solutions !

There are an infinite number of solutions.

Infinite number of solutions

it means you can never run out of possible solutions - there are an infinite number of them.

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No, this is not necessarily the case. A function can have an infinite range of solutions but not an infinite domain. This means that not every ordered pair would be a solution.

There is an infinite number of solutions to this question !

Either an infinite number or none.