Q: Does the set of a rational number have an additive identity?

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Zero is the additive identity in the set of real numbers; when you add zero to any number, the number does not change its identity.

No. A real number is only one number whereas the set of rational numbers has infinitely many numbers. However, the set of real numbers does contain the set of rational numbers.

Yes, zero is a number.Yes, zero is a number.Edit: Zero is actually not classified as a number - it is a separator. It stands for nothing. Take as an example the number One hundred and nine (109). Without the zero to separate the 100 from the 9, it would look the same as the number 19 !Edit 2: Zero IS a number and not just a separator. The set of numbers (integers or rationals or reals or complex) includes, AS A MEMBER, an additive identity such that for any member x in the set, x + i = i + x. This additive identity is denoted by the number 0. So it is very much a number.

A group containing 9.34 is a set of numbers, with some operation defined on the set that also satisfies:closure,associativity,identity, andinvertibility.Two simple groups will be the additive group of 9.34 and all its multiples (including negative ones). The identity is 0.The other is the multiplicative group consisting of all powers of 9.34 and the identity is 1.There can be a finite additive group derived from the first by defining the operation as modulo addition, and similarly with the multiplicative group.Finally, any group that contains one of these groups and also maintains the four conditions listed above, for example, all rational numbers, will also meet the requirements.

not necessarily... An integer is a rational number, but so is any real number between consecutive integers.

Related questions

There is only one set and it does have an additive identity.

Yes, it does.

Yes. The additive identity is 0.

Zero is the additive identity in the set of real numbers; when you add zero to any number, the number does not change its identity.

I t is the number 0, which has the property that x + 0 = 0 + x = x for all rational numbers x.

Wrong! Not only is zero a real number, but it is the additive identity for the set of integers, rational numbers as well as real numbers.

The additive identity for a set is a number (denoted by 0) such that a + 0 = 0 + a = a for all elements a which belong to the set.

The first number is 0, the additive identity for the set of numbers. The second, 73 is a positive integer or counting number and the third, 38.5 is a decimal representation of a rational number.

To give the set closure with respect to subtraction, or to give it an additive identity.

No. It has a different additive inverses for each element.

Yes, it does.

not a real number * * * * * Zero is very much a real number. In fact it is the additive identity for the set of real numbers.