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Yes, totally.

Number sense is a feeling of being at ease with number work, having an almost intuitive feel for what the answer of a sum might be and so forth. Number theory is the systematic study of numbers and how the various sets of numbers (counting numbers, naturals numbers, integers, rationals, irrationals, reals, complex numbers, quaternions et cetera) relate to one another. It is the study of primes and composites.

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Q: Is number theory different from number sense?
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