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> This is a factor of 4 improvement! This is a common mistake. It should read, "This is a factor of 3 improvement!" x+x+x+x is an improvement over x of 3x not of 4x. The improvement factor is 3.
> This is a factor of 4 improvement! This is a common mistake. It should read, "This is a factor of 3 improvement!" x+x+x+x is an improvement over x of 3x not of 4x. The improvement factor is 3.
I am not a native speaker, so I was always under impression that "factor of K larger" means something was X and became K * X (e.g. the multiplicative factor was 1 and became X). Can I read somewhere about the correct usage?
The general equation for an increased quantity from A to B is
increase = B - A
increase * 100
(increase + A) * 100Earlier quoted context omitted.
What exactly are you nitpicking? 1000^depth is not a constant: the function here is "f(depth) = number of times the inner loop body executes". f(depth) = O(1000^depth). And, "times" here is serving the same role as "comparisons" in "Mergesort takes O(n log n) comparisons": it's referring to the thing that f is actually counting.
Given O(f(x)), x is almost always understood to be measurement of the work input to the algorithm. Loop nesting depth is not a measurement of work input, it's a property of the code – "1000^depth" is constant for any given algorithm. Yes, O(…) is just a mathematical construct, so you can apply it the way you have to mean "the amount of work done for a given input size increases exponentially with respect to the numbe…
Earlier quoted context omitted.
I am not a native speaker, so I was always under impression that "factor of K larger" means something was X and became K * X (e.g. the multiplicative factor was 1 and became X). Can I read somewhere about the correct usage?
www.wikihow.com/Calculate-Percentage-Increase The general equation for an increased quantity from A to B is increase = B - A So a percentage increase is increase * 100 not (increase + A) * 100
See: https://ell.stackexchange.com/a/52747
Maybe my problem is that I am missing "by".
Earlier quoted context omitted.
www.wikihow.com/Calculate-Percentage-Increase The general equation for an increased quantity from A to B is increase = B - A So a percentage increase is increase * 100 not (increase + A) * 100
but I am not talking about the percentage increase I am talking about increase "by a factor of X" that is X = B/A. See: https://ell.stackexchange.com/a/52747 Maybe my problem is that I am missing "by".
B/A is the percentage of the new value relative to the old.
(B-A)/A is the percentage of the increase of the value.
This is algebra not English.
1) You start out with one rock. 2) You add another rock, getting a pile of two rocks. 3) The rock pile size is now 200% of the original size. But, the increase of the rock pile size is 100%. 4) According to the rules of algebra, 100% = 1. In this case 100% = 1 rock, since the unit under discussion is rocks.
Earlier quoted context omitted.
I am not a native speaker, so I was always under impression that "factor of K larger" means something was X and became K * X (e.g. the multiplicative factor was 1 and became X). Can I read somewhere about the correct usage?
www.wikihow.com/Calculate-Percentage-Increase The general equation for an increased quantity from A to B is increase = B - A So a percentage increase is increase * 100 not (increase + A) * 100
Earlier quoted context omitted.
but I am not talking about the percentage increase I am talking about increase "by a factor of X" that is X = B/A. See: https://ell.stackexchange.com/a/52747 Maybe my problem is that I am missing "by".
You are exactly talking about percentages. B/A is the percentage of the new value relative to the old. (B-A)/A is the percentage of the increase of the value. This is algebra not English. 1) You start out with one rock. 2) You add another rock, getting a pile of two rocks. 3) The rock pile size is now 200% of the original size. But, the increase of the rock pile size is 100%. 4) According to the rules of algebra, 100…
Earlier quoted context omitted.
You are exactly talking about percentages. B/A is the percentage of the new value relative to the old. (B-A)/A is the percentage of the increase of the value. This is algebra not English. 1) You start out with one rock. 2) You add another rock, getting a pile of two rocks. 3) The rock pile size is now 200% of the original size. But, the increase of the rock pile size is 100%. 4) According to the rules of algebra, 100…
They absolutely are not talking about percentages. They're talking about factors. A factor is a term in a multiplication. In standard US English, increasing something by a factor means to multiply it by that number. Even the GMAT uses that phrase in that way. You absolutely can split hairs on this and the phrasing can be confusing but it is absolutely understood that "increased by a factor of 4" means to multiply by…
That's absolutely wrong... When you multiply something you scale it by a factor. When you add to something you increase it.
1) 4A is 400% of A.
2) 4A in an increase of 300%.
3) 4A is an increase of 3A.
4) 4A is an increase of a factor of 3.
In the most charitable interpretation you are confusing the terms of exponential growth with linear scaling and misapplying from one to the other. A growth factor is not the same as an increase in a factor.
Earlier quoted context omitted.
They absolutely are not talking about percentages. They're talking about factors. A factor is a term in a multiplication. In standard US English, increasing something by a factor means to multiply it by that number. Even the GMAT uses that phrase in that way. You absolutely can split hairs on this and the phrasing can be confusing but it is absolutely understood that "increased by a factor of 4" means to multiply by…
>* increasing something by a factor means to multiply it by that number* That's absolutely wrong... When you multiply something you scale it by a factor. When you add to something you increase it. 1) 4A is 400% of A. 2) 4A in an increase of 300%. 3) 4A is an increase of 3A. 4) 4A is an increase of a factor of 3. In the most charitable interpretation you are confusing the terms of exponential growth with linear scalin…
https://www.beatthegmat.com/word-translation-when-x-increase...
https://www.quora.com/Mathematics-What-does-it-mean-to-incre...
https://www.macmillandictionary.com/us/dictionary/american/b...
http://mathforum.org/library/drmath/view/74439.html
https://ell.stackexchange.com/questions/52706/what-does-redu...
Earlier quoted context omitted.
>* increasing something by a factor means to multiply it by that number* That's absolutely wrong... When you multiply something you scale it by a factor. When you add to something you increase it. 1) 4A is 400% of A. 2) 4A in an increase of 300%. 3) 4A is an increase of 3A. 4) 4A is an increase of a factor of 3. In the most charitable interpretation you are confusing the terms of exponential growth with linear scalin…
Go ahead and tell that to everyone who has been using that phrase to mean what I describe. I seriously searched for a single case of someone using the phrase in the manner you're insisting is correct and came up empty. Instead, I found a large number of resources backing up what I and OP have been stating. Even many professional mathematicians acknowledge the ambiguity but agree that the phrase means to multiply. You…
Here are some other links from Google that explains why your vociferous insistence is wrong.
http://www.crackssat.com/isee/word-problems/question-250-ans...
https://english.stackexchange.com/questions/8680/how-much-ex...
https://forum.wordreference.com/threads/increase-by-a-factor...
https://books.google.com/books?id=wDKLXdzQL5AC&pg=PA182&lpg=...
http://econlog.econlib.org/archives/2010/05/the_wall_street....
In addition to the short explanation in the last link, some of the comments on that page may help shed light, such as:
I'm a college student, and for the past few years I've been an SAT
tutor to pay the bills. 95% of my students do not know how to
calculate percentage change. I spend hours teaching kids this.
They usually start to get it after working with the formula several
times, and then I show them this:
for any number "n"
100% increase = n*2 = double
200% increase = n*3 = triple
300% increase = n*4 = quadruple
...
x*100% increase = n*(x+1)