## Do real numbers form a group under multiplication?

Question: Is the set of real numbers a group under the operation of multiplication? My professor answered it by saying: No. There is no identity element (1*0=0).

## Are real numbers closed under addition and multiplication?

Real numbers are closed under addition, subtraction, and multiplication. That means if a and b are real numbers, then a + b is a unique real number, and a ⋅ b is a unique real number. For example: 3 and 11 are real numbers.

Is the set of real numbers under the operations of addition and multiplication a field?

A field is the name given to a pair of numbers and a set of operations which together satisfy several specific laws. A familiar example of a field is the set of rational numbers and the operations addition and multiplication.

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Which of the following is not a group under addition operation?

Answer: No. The set of positive integers is not a group under the operation of addition.

### Is R+ A group under multiplication?

R+ and Q+ are groups under multiplication, because the product of two positive numbers is positive, and the reciprocal of a positive number is positive.

### What types of numbers are closed under multiplication?

Answer: Integers and Natural numbers are the sets that are closed under multiplication.

When two real numbers are multiplied the result is still a real number?

Closure Property The product of any two real numbers will result in a real number. This is known as the closure property of multiplication. In general, the closure property states that the product of any two real numbers is a unique real number.

Are complex numbers a group under multiplication?

The set of integers under ordinary multiplication is NOT a group. The subset {1,-1,1,-i } of the complex numbers under complex multiplication is a group.

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## Which of the following is not a group set of natural numbers under multiplication?

Part c) The set of natural numbers with multiplication is not a group, since there is no inverse of 2: The identity is 1, so 2*x = x*2 = 1, where x is the inverse. 2x = 1 implies x = 1/2 which is not in the set of natural numbers.

## Is Z5 a group under multiplication?

The set Z5 is a field, under addition and multiplication modulo 5. To see this, we already know that Z5 is a group under addition.

Is the set of real numbers a group under multiplication?

So taking this in view, the set of real numbers is not a group under multiplication because the element 0 has no inverse in that group, as division by 0 does not make any sense. However, if you remove 0 from the set of real numbers then the resulting set will be a group with respect to multiplication.

Are the real numbers a group?