Not everyone is agreed on this but Peano's axioms, which are the basis for the axiomatic structure of numbers defines 0 as a natural number and then all other natural numbers in terms of successors.
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The first counting number is 1. There is some disagreement over the smallest natural number. It is either 0 or 1 so your answer is either 0 or 1.
The answer is 6 2 1 0 0 0 1 0 0 0.
Yes. For example: * 0 + 0 = 0 * 1/1 + (-1/1) = 0 * 1/2 + 1/3 is not equal to zero. If the second rational number is the additive inverse of the first, then yes the sum of two rational numbers can be zero. The additive inverse is that number when added to another number gives the result 0, and is denoted as the negative of the first number; the additive inverse of the number a is denoted by -(a) and is such that a + -(a) = 0. eg the additive inverse of 1/2 is -(1/2) giving 1/2 + -(1/2) = 0.
The first number in each pair must be unique.
1