Don't know about the "following" but any irrational added to its additive inverse is 0, which is rational. Therefore, the set of irrationals is not closed under addition.
An irrational number can not be expressed as a fraction as for example the square root of 2
No. For example, the sum of pi and -pi is zero, which is rational - while each of the addends is irrational.
Any of the numbers which cannot be expressed as a ratio of two integers is irrational.
no it is not
Irrational numbers are not closed under any of the fundamental operations. You can always find cases where you add two irrational numbers (for example), and get a rational result. On the other hand, the set of real numbers (which includes both rational and irrational numbers) is closed under addition, subtraction, and multiplication - and if you exclude the zero, under division.
An irrational number can not be expressed as a fraction as for example the square root of 2
No. For example, the sum of pi and -pi is zero, which is rational - while each of the addends is irrational.
Any of the numbers which cannot be expressed as a ratio of two integers is irrational.
No. For example, the square root of two plus (minus the square root of two) = 0, which is not an irrational number.
no it is not
Irrational numbers are not closed under any of the fundamental operations. You can always find cases where you add two irrational numbers (for example), and get a rational result. On the other hand, the set of real numbers (which includes both rational and irrational numbers) is closed under addition, subtraction, and multiplication - and if you exclude the zero, under division.
[ square root of (2) ] is irrational
Irrational number are NOT called surds. For example, pi is irrational but it is not a surd.Surds are a very small subset of irrational numbers.
All irrational numbers are Real numbers - it's part of the definition of an irrational number. Imaginary numbers are neither rational nor irrational. An example of a number that is both Real and irrational is the square root of two. Another example is the number pi.
Irrational numbers are decimal numbers that can't be expressed as fractions. An example is the square root of 2
An Irrational Number is a Number that cannot be converted to a Fraction and has an unstoppable amount of numbers after the decimal point. For Example, Pi is the most famous irrational number. If I didn't answer your question, search up Irrational Numbers.
Yes. Rational numbers are numbers or decimals that repeat or terminate. Irrational numbers do not. For example π is an irrational number.