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Why whole numbers require an extension?
as whole numbers does not contain negative numbers, so for denoting ( eg: deapth of the sea,etc )negative things they require an extension.
Why rational numbers require extension?
Because numbers such as pi, e and the square root of 2 are not rational.
Why do integers require an extension?
because all numbers like irrational numbers could not be included in the set of integers
Why do natural numbers need an extension?
The natural numbers are {1, 2, 3, 4, 5, 6, ...}. The ellipse (...) is to show that there are an infinite number of natural numbers that continue to get greater to infinity. The natural numbers are not enough to represent all quantities we observe in life because they do not include zero or fractions. Negative numbers and irrational numbers also serve as additional sets which we require. Finally the imaginary numbers are added to make our system complete as far as the four basic operations and powers are concerned.
Why do the natural numbers need an extension?
While natural numbers are closed with respect to addition and mulitplication, they are missing the additive identity (zero). Furthermore, they are not closed with respect to two of the fundamental operations of arithmetic: subtraction and division.
Are there infinitely many natural numbers that are not prime?
This can be an extension to the proof that there are infinitely many prime numbers. If there are infinitely many prime numbers, then there are also infinitely many PRODUCTS of prime numbers. Those numbers that are the product of 2 or more prime numbers are not prime numbers.
Why do whole number require an extension?
The set of whole numbers is not closed under division (by non-zero whole numbers).
What natural numbers could you round to the nearest tenth to get 28?
A natural number does not require rounding to a tenth because it is already rounded, not just to a tenth but to a unit.
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 intersection between rational numbers and natural numbers?
It is the set of natural numbers.
What are the difference between natural numbers and irrational numbers?
All natural numbers are rational numbers. No irrational numbers are natural numbers.
Why natural numbers need to be extend?
The natural numbers are {1, 2, 3, 4, 5, 6, ...}. The ellipse (...) is to show that there are an infinite number of natural numbers that continue to get greater to infinity.The natural numbers are not enough to represent all quantities we observe in life because they do not include zero or fractions. Negative numbers and irrational numbers also serve as additional sets which we require. Finally the imaginary numbers are added to make our system complete as far as the four basic operations and powers are concerned.
