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What do the numbers 981 and 743 have in common?
They are 3-digit positive integers.
What are all the factors of the Numbers's?
The factors of a number comprises all positive integers which go into it evenly.
All multiples of odd natural number can be written as the sum of consecutive natural numbers?
No. Odd numbers can be written as the sum of consecutive integers, but some multiples of odd numbers are even.
Is the cardinality of an infinitely countable set the same as the rational numbers?
Yes. There is an injective function from rational numbers to positive rational numbers*. Every positive rational number can be written in lowest terms as a/b, so there is an injective function from positive rationals to pairs of positive integers. The function f(a,b) = a^2 + 2ab + b^2 + a + 3b maps maps every pair of positive integers (a,b) to a unique integer. So there is an injective function from rationals to integers. Since every integer is rational, the identity function is an injective function from integers to rationals. Then By the Cantor-Schroder-Bernstein theorem, there is a bijective function from rationals to integers, so the rationals are countably infinite. *This is left as an exercise for the reader.
Is the is the least common factor of a set of numbers always equal to one of the numbers in the set?
The least common factor of any two or more positive integers is always 1.
Is positive integers belong to natural numbers?
Positive integers are (not is!) a proper subset of natural numbers. The natural numbers comprise positive integers and zero.
Another name for the positive integers?
The natural numbers are the same as the positive integers.
Are natural numbers subsets of integers?
Yes, the natural numbers are positive integers. {1,2,3,....}
How are integers and natural numbers different?
Integers are all positive and negative whole numbers, and natural numbers are all positve whole numbers including zero. So, natural numbers is a subset of integers.
Can you said that naturl numbers is equivalent to integer?
No, because there are no naturl numbers.But natural numbers (even), are not equivalent to integers: they are a subset of integers. Negative whole numbers are integers but they are not natural numbers. Mathematicians are undecided about whether or not zero is a natural number.
Are decimals natural numbers?
No. Natural numbers are the positive integers: 1, 2, 3, ...
Is -62 a natural number?
No. Natural numbers are 0 and positive integers.
Are integers and natural numbers equivalent sets?
No, they are not equivalent sets.
Are natural numbers counting numbers and positive numbers different names for the same set of numbers?
Natural numbers are the same as counting numbers, but the term positive numbers means something else. Natural or counting numbers are positive integers, but the category of positive numbers includes both integers and fractions, as long as they are greater than zero.
Are decimals considered a natural number?
No. Decimals come under "real numbers" and not natural numbers as natural numbers are positive whole numbers i.e., positive integers.
What set of integers list the natural numbers?
Traditionally, the set of integers that represents the natural numbers is {1,2,3,...}, which are the positive integers. Some people include the non-negative integers as the set of natural numbers, which is {0,1,2,3,...}, and includes 0.
When do you use positive integers?
The set of natural numbers (counting numbers) {1,2,3,4....} corresponds to the positive integers. Note that the number 0 is neither positive nor negative. So anytime you want to count something you use natural numbers, which means you are also using positive integers.
