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Write a definition for the the Associative Property of Multiplication in your own words and explain how you would use it to compute 4x25x27 mentally.?
the property which states that for all real numbers a,b,and c their product is always the same, regardless of their grouping
Are there irrational numbers that are not real numbers?
An imaginary number i is defined as the square root of -1, so if you have something like the square root of -2, the answer would be i root 2, and that would be considered an irrational non-real number.* * * * *Not quite. The fact that irrational coefficients can be used, in conjunction with i to create complex numbers (or parts of complex numbers) does not alter the fact that all irrational numbers are real numbers.
Why are irrational numbers important?
pi and e are irrational numbers. Without them most of geometry, trigonometry, calculus or probability distributions would not be defined.
What is the intersection of the rational and irrational numbers?
There isn't any. If there were, then the intersection would consist of all the numbers that are both rational and irrational, and there aren't any of those.
Are there fewer rational numbers than irrational numbers?
For any given subset, yes, because there are an infinite number of irrational numbers for each rational number. But for the set of ALL real numbers, both are infinite in number, even though the vast majority of real numbers would be irrational.
all numbers that can be written on the number line that include rational and irrational numbers?
That would be the real numbers.
What is the intersection of the rational numbers and the irrational numbers?
Some would say that there is no intersection. However, if the set of irrational numbers is considered as a group then closure requires rationals to be a proper subset of the irrationals.
If x is irrational what would x be if x squared is irrational?
I don't knw all the possible numbers, but π is an example. π2 is irrational such as π.
Would the difference between two irrational numbers is always going to be rational?
No. sqrt(3) - sqrt(2) is irrational.
Is the set of irrational numbers closed under subtraction?
No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction: pi - pi = 0. pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number as well, which it isn't. Therefore the set of irrational numbers is NOT closed under subtraction.
What is four irrational numbers closest to 6 on the number line?
Irrational numbers are infinitely dense. Between any two numbers, there are infinitely many irrational numbers. So if it was claimed that some irrational, x, was the closest irrational to 6, it is possible to find an infinite number of irrationals between 6 and x. Each one of these infinite number of irrationals would be closer to 6 than x. So the search for the nearest irrational must fail.
What is the inational numbers?
Irrational numbers are not able to be formed from a simple ratio or fraction.The root word behind rational is the word Ratio, the relationship of two numbers. Their ratio.Pi and e would be common irrational numbers, as is 2^0.5
