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Q: Why every nonempty subset of the negative integers has a greatest element?
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What are the three categories of integers?

The set of integers is divided into three subsets. One is the positive integers. Another is the negative integers. The last subset has one element -- zero. In sum, integers are composed of the positive integers, the negative integers, and zero.


Is zero an element of all integers?

Yes.....0 is an element of all integers Integers can be thought of as points on an infinitely long number line


If a number is an element of the set of the rational numbers is it also an element of the set of integers?

No.


Is a negative number an integer?

Integers are all of the real numbers that can be written without using a decimal or a fraction; i.e, they're the set of all positive and negative whole numbers plus zero.Integers have the following properties:i) 0 exists, and is the additive identity element; 0 + a = a for all a.ii) 1 exists, and is the multiplicative identity element; 1a = a for all a.iii) Addition and multiplication are both associative and commutative.iv) An additive inverse exists for all elements a, denoted as -a.v) Distributivity.vi) Adding or multiplying two integers yields another integer.From iv), we know that for each a > 0, there exists an additive inverse, -a, which must be less than 0, hence a negative number.So, there are integers that are negative numbers.But, not every negative number is an integer. There are negative numbers that must be expressed as a decimal or a fraction. For example, -0.5 isn't an integer, because, were you to not write it as a decimal, you would have to write it as a fraction: -1/2


Which element has the greatest average atomic mass?

Ununoctium.

Related questions

What are the three categories of integers?

The set of integers is divided into three subsets. One is the positive integers. Another is the negative integers. The last subset has one element -- zero. In sum, integers are composed of the positive integers, the negative integers, and zero.


Is zero an element of all integers?

Yes.....0 is an element of all integers Integers can be thought of as points on an infinitely long number line


What is a set of numbers that includes 1 but not zero?

The set of positive integers contains 1 but not zero. Within the set of integers, there is the subset of positive integers, the subset of negative integers and the subset with a single element in it - zero. There are a zillion other sets that could be specified that meet the conditions set down in the question. The one cited is an easy one.


The element that has the greatest electromagnetivity is?

Fluorine is the element that has the greatest electronegativity on the periodic table.


If a number is an element of the set of the rational numbers is it also an element of the set of integers?

No.


If a number is a element of the set or rational numbers is ig also an element of the set of integers?

That is not true.


Is set of integers is a group under multiplication?

No. One of the group axioms is that each element must have an inverse element. This is not the case with integers. In other words, you can't solve an equation like: 5 times "n" = 1 in the set of integers.


Is 0 an element of I the set of integers true or false?

It is true.


Is a negative number an integer?

Integers are all of the real numbers that can be written without using a decimal or a fraction; i.e, they're the set of all positive and negative whole numbers plus zero.Integers have the following properties:i) 0 exists, and is the additive identity element; 0 + a = a for all a.ii) 1 exists, and is the multiplicative identity element; 1a = a for all a.iii) Addition and multiplication are both associative and commutative.iv) An additive inverse exists for all elements a, denoted as -a.v) Distributivity.vi) Adding or multiplying two integers yields another integer.From iv), we know that for each a > 0, there exists an additive inverse, -a, which must be less than 0, hence a negative number.So, there are integers that are negative numbers.But, not every negative number is an integer. There are negative numbers that must be expressed as a decimal or a fraction. For example, -0.5 isn't an integer, because, were you to not write it as a decimal, you would have to write it as a fraction: -1/2


What is the fifth period transition element with greatest atomic number?

The fifth period transition element with the greatest atomic number is tantalum (element 73).


Which element has the greatest density at STP?

i dont now


What is the sign for Integers?

It can be displayed as 'Z'. So we can say every integer is an element of Z. n ε Z means all ' n ' are integers.