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If you mean between 1 and 10 inclusive, then there's 10: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
If you mean exclusive, then there's 8: 2, 3, 4, 5, 6, 7, 8, 9
If you mean inclusive of one of the boundaries, then there's 9: 1, 2, 3, 4, 5, 6, 7, 8, 9
Including decimal places, then no matter what inclusive method or otherwise, there is an infinite number of numbers between one and ten.
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