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Q: What is nonnegative integer?

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The least non negative integer would be 1.

Yes but a double negative integer is also positive as for example --2 = +2

No. It is nonnegative. Zero is neither positive nor negative.

No. 0 is a non-negative integer which is not positive.

There is no smallest integer, as the integers continue in the negative direction to infinity. The smallest nonnegative integer is 0 (zero).

It is indeed. A whole number is a nonnegative integer: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9...

The absolute value of a number is always nonnegative.

1

True.

The set of nonnegative integers is the set {0, 1, 2, 3, 4, 5, 6, ...} Each number in this set is an "example".

The unique nonnegative square root of a nonnegative real number. For example, the principal square root of 9 is 3, although both -3 and 3 are square roots of 9.

A polynomial is a function which can take the form: f(x) = sum(a_n * x^n) where n is a nonnegative integer. 0 is the constant function which can be represented in the form above by taking a_n = 0 for all n.

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