# Understanding Inverses & Max* for Integers

• kathrynag
In summary, the conversation discusses determining if an inverse exists for a group defined on the integers using different operations. The first operation is defined as a*b=ab, and it is concluded that an inverse does not exist within the group. The second operation is defined as a*b=max{a,b}, and the properties of associativity and identity are checked to see if it is a group, but it is ultimately determined that there is no inverse for this operation.
kathrynag

## Homework Statement

If I have a group defined on the integers, by a*b=ab, how do I know if an inverse exists?
Also, define * on the integers by a*b=max{a,b}

## The Attempt at a Solution

I got 1/a as an inverse, but I'm thinking it's not a group since we don't know if 1/a is an element of the integers.

The max is confusing me.
I know I need to check associativity, identity, and inverse for a group.
a*(b*c)=a*max{b,c)
=max{a,max{b,c}}
(a*b)*c=max{a,b}*c
=max{max{a,b},c}
I'm already confused at this point.

you only need contradict one of the properties for it not to be a group

The first one is correct, for a not equal to e, the inverse does not exist within the group.

For the 2nd
associativity is ok, as max{max{a,b},c} = max{a,b,c}
you could try the identity, whici si clearly not unique
or probably more straight forward show there is no inverse, consider a*b with a<b

## 1. What is an inverse of an integer?

An inverse of an integer is a number that, when multiplied by the original integer, results in a product of 1. For example, the inverse of 5 is 1/5, because 5 x 1/5 = 1. Inverses are often denoted by the exponent -1, so the inverse of 5 would be written as 5-1.

## 2. How do you find the inverse of an integer?

To find the inverse of an integer, you can use the formula a-1 = 1/a, where a is the original integer. For example, to find the inverse of 5, you would use the formula 5-1 = 1/5, which gives an inverse of 1/5.

## 3. What is the importance of understanding inverses for integers?

Understanding inverses for integers is important because it allows us to solve equations involving multiplication and division more easily. Inverses also play a key role in many mathematical concepts, such as fractions, decimals, and rational numbers.

## 4. What is the maximum value for an integer?

The maximum value for an integer depends on the data type being used. In 32-bit systems, the maximum value for an integer is 2,147,483,647. In 64-bit systems, the maximum value is 9,223,372,036,854,775,807.

## 5. How does understanding inverses and max for integers relate to real-world applications?

Understanding inverses and max for integers is important in many real-world applications, such as calculating interest rates, determining proportions in cooking and baking, and analyzing data in scientific research. Additionally, understanding the maximum value of integers is crucial in computer programming and data storage.

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