A finite set is a set that has numbers you can count. Its not like infinite with no end it has an end.
no
No; there are infinitely many rational numbers.
This is called a discrete set (all points isolated) or a finite set. Finite sets are always discrete.
Finite sets:The counting numbers up to 10{1, 2, 3}The integer factors of 48The members of my immediate familyThe people on EarthThe grains of sand on planet EarthCountable infinite sets:The set of integersThe set of prime numbersThe set of square numbersThe set of rational numbersUncountable infinite sets:The set of real numbersThe set of complex numbers
The empty set is a finite set.
A finite set is a set that has numbers you can count. Its not like infinite with no end it has an end.
The set of your friends is finite. The set of counting numbers (part of which you will use to count your friends) is infinite.
no
No; there are infinitely many rational numbers.
Euclid (c. 300 BC) was one of the first to prove that there are infinitely many prime numbers. His proof was essentially to assume that there were a finite number of prime numbers, and arrive at a contradiction. Thus, there must be infinitely many prime numbers. Specifically, he supposed that if there were a finite number of prime numbers, then if one were to multiply all those prime numbers together and add 1, it would result in a number that was not divisible by any of the (finite number of) prime numbers, thus would itself be a prime number larger than the largest prime number in the assumed list - a contradiction.
Finite.
The LCM of a set of prime numbers is their product.
This is called a discrete set (all points isolated) or a finite set. Finite sets are always discrete.
Finite sets:The counting numbers up to 10{1, 2, 3}The integer factors of 48The members of my immediate familyThe people on EarthThe grains of sand on planet EarthCountable infinite sets:The set of integersThe set of prime numbersThe set of square numbersThe set of rational numbersUncountable infinite sets:The set of real numbersThe set of complex numbers
There is an infinite set of prime numbers.
Start with the set of Natural numbers = N.Combine these with negative natural numbers and you get the set of Integers = Z.Combine these with ratios of two integers, the second of which is positive, and you get the set of Rational numbers = Q.Start afresh with numbers which are not rational, nor the roots of finite polynomial equations. This is the set of transcendental numbers.Combine these with the non-rational roots of finite polynomial equations and you have the set of Irrational Numbers.Combine the rational and irrational numbers and you have the set of Real numbers, R.