re: Do you think space is infinite?

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Can someone clarify something for me... I keep seeing people say they think the universe is expanding constantly, yet it's not infinite.

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Expansion does not equate with infinity. Expansion can stop. It began after spacetime inflated. It will continue until every atom and its components achieve total entropy or until spacetime ceases inflation. It seems that Dark Energy is driving expansion within spacetime. What is driving inflation is unknown. It may be that inflation has or will achieve a maximum and then contract. There are no good theories.

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Isn't the definition of infinity a number that never ceases expansion

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In general, infinity is the quality or state of endlessness or unboundedness in terms of space and time. The Standard Model of physics does not allow for infinity.