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Numerical Concepts : Definitions

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Please explain or define these concepts.

1. Natural number

2. Multiplication

3. Subtraction

4. Closure for addition

5. Commutativity

6. Associativity

7. Distributivity

8. Closure for multiplication

9. Contrast commutativity and associativity

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Concepts and definitions are provided. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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1. N = {1, 2, 3. .. } these are just the counting numbers

2. multiplication is a basic arithmetic operation

for natural numbers m, and n, multiplication of m and n is the repeated sum of the other number

mn = n + .. + n (m times)

equivalently,

mn = m + .. + m (n times)

3. subtraction is ...

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