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Is the distance between two real numbers p and q equal to the absolute value of p and q?
Wiki User
∙ 11y ago
No.
First, the answer depends on how distance is defined. There are many ways of defining metrics.
With the common definition "Euclidean distance", in 2 or more dimensions, the distance between P and Q is calculated using the generalised form of Pythagoras's theorem.
Thus, if P = (p1, p2, ..., pn) and Q = (q1, q2, ... , qn) are the coordinates of points P and Q in n-dimensional space, then the distance PQ is qiven by
|PQ|2 = (p1 - q1)2 + (p2 - q2)2 + ... + (pn - qn)2
and so |PQ| is the principal square root of the above.
In 1-dimensional space (along a line), this simplifies to
|PQ|2 = (p1 - q1)2
so that
|PQ| = |p1 - q1| and this will always be less than or equal to abs(p and q).
Wiki User
∙ 11y ago
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What numbers have equal absolute values?
A positive and negative number with the same magnitude (value) will have their absolute values equal.
Will the square of a numbers absolute value always equal the absolute value of the number's square?
yes
Is the sum of an absolute value is the same of their absolute values?
The sum of the absolute values of two numbers is greater or equal than the absolute values of the sum. It will be equal if both are positive or both are negative; greater if one is positive and one is negative. Try it out with some sample numbers!
Will positive numbers alway have a higher absolute value than the negative numbers?
No, positive numbers do not always have a higher absolute value than negative numbers. The absolute value of a negative number is equal to its positive equivalent. For example, the absolute value of -3 and 3 is both 3.
Is the standard deviation the same as the mean of absolute distances from the mean?
no the standard deviation is not equal to mean of absolute distance from the mean
What are Two numbers at equal distance from zero are called?
Absolute value
What do you call two numbers that are equal distance from zero on a number line?
That is called Absolute Value
What are two numbers the same distance from zero on the number line?
Numbers the same distance from zero (linearly) have the same "absolute value" whether positive or negative.
Why is absolute value used to find distances on a coordinate plane?
This is because the distance between two points is always greater than or equal to zero - a property of absolute numbers.
What numbers have equal absolute values?
A positive and negative number with the same magnitude (value) will have their absolute values equal.
Is there any way to calculate the absolute value of a complex number that equals a negative number?
Given that absolute values are always positive, and that there is no equivalence between complex numbers and real numbers, I would have to say no, there isn't. The absolute value of a real number is its distance from zero on a number line. Since a distance is always positive, we say the absolute value is always positive. Graphically, a real number is just a point on a number line. The absolute value of a complex number is its distance form the origin in a coordinate plane, where coordinate axes are the x-axis with real numbers, and the y-axis with imaginary numbers. In this diagram, called Argand diagram, a complex number a + bi (where a and b are real numbers) is the point (a, b) or the vector from the origin to the point (a, b). Using the distance formula, the absolute value or the distance of a complex number a + bi is equal to the principal square root of (a2 + b2).
Will the square of a numbers absolute value always equal the absolute value of the number's square?
yes
Is the sum of an absolute value is the same of their absolute values?
The sum of the absolute values of two numbers is greater or equal than the absolute values of the sum. It will be equal if both are positive or both are negative; greater if one is positive and one is negative. Try it out with some sample numbers!
Will positive numbers alway have a higher absolute value than the negative numbers?
No, positive numbers do not always have a higher absolute value than negative numbers. The absolute value of a negative number is equal to its positive equivalent. For example, the absolute value of -3 and 3 is both 3.
Is the standard deviation the same as the mean of absolute distances from the mean?
no the standard deviation is not equal to mean of absolute distance from the mean
Why do birds roosting on a electrical wire have an equal distance between them?
They have equal distance between them to keep balance.
How many numbers have an absolute value equal to 5?
on the real number line there are 2 values with |5|, ie +5 and -5. on the complex plane there are an infinite set of values with an absolute value of 5, ie all the points of distance 5 from the origin.
