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What is the states that an infinite number of rational numbers can be found between any two rational numbers?
That is the property of infinite density of rational numbers. If x and y are any two rational numbers then w = (x + y)/2 is a rational number between them. And then there is a rational number between x and w. This process can be continued without end.
What is the example rational numbers?
Given any two integers, x and y, such that y is not 0, then x/y is a rational number. So for example, 3476/43 is a rational number.
What is the difference between integer and rational numbers?
An integer is a whole number: a countng number, zero or a negative counting number. That is, an element of the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. A rational number is one that can be expressed in the form x/y where x and y are integers, and y is not zero.
Is Y over Y irrational?
No because y/y is equivalent to 1 which is a rational number
A rational number is a natural number?
A natural number is an integer equal to 1 or greater. A rational number can be an integer or a fraction represented as x/y whereby x and y are both integers.
What is the states that an infinite number of rational numbers can be found between any two rational numbers?
That is the property of infinite density of rational numbers. If x and y are any two rational numbers then w = (x + y)/2 is a rational number between them. And then there is a rational number between x and w. This process can be continued without end.
If x is a rational number and y is a rational number than is x plus y rational?
If both numbers are rational then x plus y is a rational number
Show that the sum of rational no with an irrational no is always irrational?
Suppose x is a rational number and y is an irrational number.Let x + y = z, and assume that z is a rational number.The set of rational number is a group.This implies that since x is rational, -x is rational [invertibility].Then, since z and -x are rational, z - x must be rational [closure].But z - x = y which implies that y is rational.That contradicts the fact that y is an irrational number. The contradiction implies that the assumption [that z is rational] is incorrect.Thus, the sum of a rational number x and an irrational number y cannot be rational.
If you add a rational and irrational number what is the sum?
an irrational number PROOF : Let x be any rational number and y be any irrational number. let us assume that their sum is rational which is ( z ) x + y = z if x is a rational number then ( -x ) will also be a rational number. Therefore, x + y + (-x) = a rational number this implies that y is also rational BUT HERE IS THE CONTRADICTION as we assumed y an irrational number. Hence, our assumption is wrong. This states that x + y is not rational. HENCE PROVEDit will always be irrational.
What is the different between a rational and irrational number?
Rational numbers can be represented in the form x/y but irrational numbers cannot.
Is 65.4279 a rational number?
Yes, it is.
What is the example rational numbers?
Given any two integers, x and y, such that y is not 0, then x/y is a rational number. So for example, 3476/43 is a rational number.
Is -9 a rational or irrational number?
Rational. A rational number, z, is any number that can represented in the formx/y = z
How do you find a rational number between two rational numbers?
Suppose the two rational numbers are x and y.Then (ax + by)/(a+b) where a and b are any positive numbers will be a number between x and y.
What is the difference between integer and rational numbers?
An integer is a whole number: a countng number, zero or a negative counting number. That is, an element of the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. A rational number is one that can be expressed in the form x/y where x and y are integers, and y is not zero.
Proof that square of any rational number is rational?
Consider a rational number, p.p is rational so p = x/y where x and y are integers.x is an integer so x*x is an integer, and y is an integer so y*y is an integer.So p2 = (x/y)2 = x2/y2 is a ratio of two integers and so is rational.
If x is rational and y is rational then xy is rational?
Yes, the product of two rational numbers is always a rational number.
