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.
people
Since there is an infinite number of real numbers and an infinite number of natural numbers, there is not more of one kind than of another.
Yes.
Yes, there is an infinite amount of prime numbers. This has been proven by the ancient Greek mathematician Euclid. As for composite numbers, since there are infinitely many natural numbers, there must also be an infinite amount of composite numbers, as they are all the natural numbers that are not prime.
There are an infinite amount of numbers that have a greater difference than 1,000
No.
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.
Numbers are infinite, as a matter of fact counting decimals there are a infinite amount of numbers between 0 and 1. So depending on what you mean with natural numbers no, there is no natural last number.
All natural numbers are rational numbers. No irrational numbers are natural numbers.
-- There's an infinite number of rational numbers. -- There's an infinite number of irrational numbers. -- There are more irrational numbers than rational numbers. -- The difference between the number of irrational numbers and the number of rational numbers is infinite.
The only difference is that whole numbers include 0 (zero), while natural numbers start with 1 (one). That's it!
people
Since there is an infinite number of real numbers and an infinite number of natural numbers, there is not more of one kind than of another.
Yes.
There are an infinite set of pairs of numbers which have a difference of two.
Yes, there is an infinite amount of prime numbers. This has been proven by the ancient Greek mathematician Euclid. As for composite numbers, since there are infinitely many natural numbers, there must also be an infinite amount of composite numbers, as they are all the natural numbers that are not prime.
There are an infinite amount of numbers that have a greater difference than 1,000