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Every nonempty subset of the negative integers has a greatest element because the set of negative integers is well-ordered by the standard order of integers. This means that for any nonempty subset of negative integers, there exists a least upper bound, which is the greatest element in that subset. Since negative integers are ordered, any nonempty subset will always contain an element that is less than or equal to all other elements in that subset, ensuring the presence of a greatest element.
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What is the smallest element in the set of integers?
The smallest element in the set of integers is negative infinity, as integers extend indefinitely in the negative direction. However, if considering the set of integers as whole numbers, the smallest integer is -∞.
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.
What are whole numbers and their opposites and zero?
Whole numbers are the set of non-negative integers that include zero and all positive integers, such as 0, 1, 2, 3, and so on. Their opposites are the corresponding negative integers, which are -1, -2, -3, etc. Zero is unique in this set as it is neither positive nor negative, serving as the neutral element in addition. Together, whole numbers and their opposites form a broader set known as integers.
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 the characteristics of each set of numbers that make up the set of integers?
The set of integers consists of three distinct subsets: positive integers (1, 2, 3, ...), negative integers (-1, -2, -3, ...), and zero (0). Positive integers are whole numbers greater than zero, while negative integers are whole numbers less than zero. Together, these subsets form a continuous, infinite set that includes both positive and negative values, as well as zero, which serves as a neutral element in addition and subtraction. Integers do not include fractions or decimals, emphasizing their characteristic as whole numbers.
What is the smallest element in the set of integers?
The smallest element in the set of integers is negative infinity, as integers extend indefinitely in the negative direction. However, if considering the set of integers as whole numbers, the smallest integer is -∞.
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.
What are whole numbers and their opposites and zero?
Whole numbers are the set of non-negative integers that include zero and all positive integers, such as 0, 1, 2, 3, and so on. Their opposites are the corresponding negative integers, which are -1, -2, -3, etc. Zero is unique in this set as it is neither positive nor negative, serving as the neutral element in addition. Together, whole numbers and their opposites form a broader set known as integers.
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 the characteristics of each set of numbers that make up the set of integers?
The set of integers consists of three distinct subsets: positive integers (1, 2, 3, ...), negative integers (-1, -2, -3, ...), and zero (0). Positive integers are whole numbers greater than zero, while negative integers are whole numbers less than zero. Together, these subsets form a continuous, infinite set that includes both positive and negative values, as well as zero, which serves as a neutral element in addition and subtraction. Integers do not include fractions or decimals, emphasizing their characteristic as whole numbers.
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.
If a number is an element of the set of the rational numbers is it also an element of the set of integers?
No.
The element that has the greatest electromagnetivity is?
The element that has the greatest electromagnetivity is Flourine, F, with 3.98.
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.
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 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
