In math, we constantly need to derive various algorithms to gain a tighter error bound. It might be correct virtually surely that: the error bound of B is much better than that of A by a aspect x (x is bigger than 1). However, i am not sure if it is best to say: the error bound of A is weaker 보다 that of B by a factor x (x is samller than 1)?


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If B is better than A by a element of x, climate A is weaker 보다 B through a aspect of x.

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Not only is that correct, but it is tantamount to this statement:

If B == A * x, then A == B / x

There have to be no border on x though. No have to say (x bigger 보다 1) or (x smaller than 1). Everything x is in one statement, it must be the exact same in the other.

Take the starting statement: B is much better than A by a element of x. What "better" method can be confusing due to the fact that it is unique to your exact problem, so I"ll just use the value (rather 보다 the algorithm) that B and compare that with the value the A.

Now we have: B > A by a aspect of X.

The expression "by a variable of, way when either increasing or to decrease a worth by multiplying it by some factor. Due to the fact that we room measuring just how "good" an algorithm is, we aren"t simply comparing two numbers on the normal scale.If we have a logarithmic scale (base 10) wherein 5 is the worst one algorithm can perform, and also 8 is the ideal an algorithm have the right to perform, climate the values 6 is better than the worth 5 by a aspect of 10. Similarly, 5 is worse than 6 through a variable of 10.

Below I provide links and show details around how to uncover this equation, however in this section I"ll just solve it.

If we have some initial value, i, and we rise it through a variable of some unknown, x, and we finish at some last value, f, we deserve to solve for the factor:

(f / i) == fIf we had lessened i by a aspect of x and ended in ~ f, we can solve for the factor like this:

(f / i) == (1 / f)See the station relationship?

We have the right to use this to present that A is weaker than B by a element of X.

Initial worth = AFinal worth = BFactor = X(A / B) = X(B / A) = 1 / XSo to get the factor, when we boost A by a variable of X to obtain to B, we find the element is X. And if we decrease through a factor, i.e. Go from B come A, we take the inverse and see the variable is 1/X.

If we give X a number, let"s speak 5, we can see the home in action:

(A / B) = 5 => A = 5B(B / A) = (1 / 5) => B = 1/5AYou can plug in either value of A or B right into the various other equation to see they are both true.

The consumption of saying that some value is decreased by a variable of some value isn"t too typical in pure math (excluding grammar school math), however you carry out see the in branches prefer economics and physics.

See the definition of factor follow to the Cambridge Dictionary"s listing:

a ​number or ​variable (= ​letter or ​symbol) the is gift ​multiplied in a ​product (= ​result the ​multiplying):

According come this definition, a factor is simply some number or variable gift multiplied to another.

We can use the meaning of "factor" to see how the following examples make sense:

Suppose you invest $100, and after a time, your invest was precious $300. The final value ($300) would certainly be three (3) time the early value. We would certainly say that your investment had increased by a factor of 3.

On the various other hand, if girlfriend made a bad investment, and the value decreased from $100 come $25, then the final value would certainly be a 4 minutes 1 (1/4) the the early value. We would certainly say the invest had decreased by a aspect of 4.

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This short short article goes top top to show how the last value separated by the initial worth is same to the variable when increasing a value by a factor. It additionally shows the element is the reciprocal of that value when decreasing by a factor.