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What is the relationship between natural numbers and real numbers?
Wiki User
∙ 13y ago
In mathematics, natural numbers are the ordinary counting numbers 1, 2, 3, ... (sometimes zero is also included). Since the development of set theory by Georg Cantor, it has become customary to view such numbers as a set. There are two conventions for the set of natural numbers: it is either the set of positive integers {1, 2, 3, ...} according to the traditional definition; or the set of non-negative integers {0, 1, 2, ...} according to a definition first appearing in the 19th century.
Natural numbers have two main purposes: counting ("there are 6 coins on the table") and ordering ("this is the 3rd largest city in the country"). These purposes are related to the linguistic notions of cardinal and ordinal numbers, respectively. (See English numerals.) A more recent notion is that of a nominal number, which is used only for naming.
Properties of the natural numbers related to divisibility, such as the distribution of prime numbers, are studied in number theory. Problems concerning counting and ordering, such as partition enumeration, are studied in combinatorics.
Wiki User
∙ 13y ago
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What are differences between natural numbers and real numbers?
Natural numbers extend from 1 to positive infinity.Real numbers are all numbers between negative infinity and positive infinity.ALL natural numbers are real numbers, but NOT ALLreal numbers are natural numbers.
What do you mean by countably infinite and infinite?
Countably infinite means you can set up a one-to-one correspondence between the set in question and the set of natural numbers. It can be shown that no such relationship can be established between the set of real numbers and the natural numbers, thus the set of real numbers is not "countable", but it is infinite.
Are natural numbers real numbers?
Yes, all natural numbers are real numbers. Natural numbers are a subset of real numbers, so not all real numbers are natural numbers.
What is the relationship between real numbers integers rational and irrational numbers and whole numbers?
They are all numbers
What is the relationship between real number and rational number?
Rational numbers form a proper subset of real numbers. So all rational numbers are real numbers but all real numbers are not rational.
Are real numbers natural numbers?
No. Natural numbers are a proper subset of real numbers.
Are real numbers a subset of natural numbers?
No because natural numbers are a subset of real numbers
What is the relation between integers natural numbers whole numbers rational and irrational numbers?
Natural numbers = Whole numbers are a subset of integers (not intrgers!) which are a subset of rational numbers. Rational numbers and irrational number, together, comprise real numbers.
What is the difference between natural infinite numbers and real infinite numbers?
A natural number is a counting number, such as 1, 2, 3. There are also known as whole numbers and integers. They can be infinitely large. A real number is a number, possibly a natural number, but more possibly not, because there are an infinite number of real numbers that lie between any two natural numbers, such as 1, 1.1, 1.11, 1.111, 111112, etc, ad infinitum. Real numbers can also be infinitely large.
Can a number be a natural number and a real number?
All natural numbers are also real numbers, but all real numbers are not necessarily natural numbers because natural numbers are positive whole numbers. Real numbers are any number on the number line, which includes irrational numbers like pi and sqrt2. Thus only the positive natural numbers are both natural and real. Hope this is not too long-winded!
What are all the natural numbers?
All the positive real numbers are natural numbers.
What is a natural number that is not real?
The set of Natural Numbers is the set of 'counting numbers' {1,2,3,4,....}. All of them are also real numbers.
