Scrabble Dictionary

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Yes, integer is playable

...and is worth 10 points.

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TWL06 (NASPA List 2006)

"Integer" Definition

noun

Mathematics A complete unit or entity.
Mathematics A member of the set of positive whole numbers {1, 2, 3, . . . }, negative whole numbers {-1, -2, -3, . . . }, and zero {0}.
Any of the natural numbers, the negatives of these numbers, or zero.
A complete entity.