Multiply them together.
Count the number of negative numbers. If this is an even number, the sign is + and if it is odd, the sign is -.
The sum of two rational numbers is rational.From there, it follows that the sum of a finite set of rational numbers is also rational.
No. The set of real numbers contains an infinitely more irrational numbers than rational numbers.
The answer requires a bit of mathematics, but goes like this:The product of any 2 rational numbers is a rational number.The product of any 2 irrational number is an irrational number.The product of a rational and an irrational number is an irrational number!Therefore simple logic tells us that there are more irrational numbers than rational numbers. There is a way to structure this mathematically, and I believe it is called an "Inductive Proof".Interesting !I'm going to say "No".I reason thusly:-- For every rational number 'N', you can multiply or divide it by 'e', add it to 'e',or subtract it from 'e', and the result is irrational.-- You can multiply or divide it by (pi), add it to (pi), or subtract it from (pi),and the result is irrational.-- You can take its square root, and more times than not, its square root is irrational.There may be others that didn't occur to me just now. But even if there aren't,here are a bunch of irrational numbers that you can make from every rational one.This leads me to believe that there are more irrational numbers than rational ones.-------------------------------------------------------------------------------------------------------There are infinitely many more irrationals than rationals; this was proved by G. Cantor (born 1845, died 1918). His proof is basically:The rational numbers can be listed by assigning to each of the counting numbers (1, 2, 3,...) one of the rational numbers in such a way that every rational number is assigned to at least one counting number;If it is assumed that every irrational number can be assigned to at least one counting numbers (like the rationals), then with such a list it is possible to find an irrational number that is not on the list; so is it not possible as there are more irrationals than there are counting numbers, which has shown to be the same size as the rational numbers, thus showing that there are more irrationals than rationals.
Multiply them together.
Count the number of negative numbers. If this is an even number, the sign is + and if it is odd, the sign is -.
Two or more numbers are needed to find their product
The sum of two rational numbers is rational.From there, it follows that the sum of a finite set of rational numbers is also rational.
There are more irrational numbers between any two rational numbers than there are rational numbers in total.
Two or more numbers are needed to find their product in multiplication.
Two or more numbers are normally needed to find the product
Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.Infinitely many. In fact, there are more irrational numbers between them than there are rational numbers.
Every odd or even number is a rational number, and there are a lot more rational numbers besides those.
Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)Both are part of the real numbers; both are infinite sets. (However, there are more irrational than rational numbers.)
The short answer to your question: yes. This is one of the central axioms of math. If you'd like a bit more detail, try researching number theory.
No. In fact, there are infinitely more irrational numbers than there are rational numbers.