Wikipedia:Reference desk/Archives/Mathematics/2011 May 29

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May 29

is the difference between 1x and 3x 2x or 3x?

title says it all... is the difference between 1x and 3x 2x or 3x? for example, engine speed. 188.156.253.51 (talk) 00:44, 29 May 2011 (UTC)

I do not understand the question, could you expand please. What do they mean and why would they be written with different numbers if they mean the same thing? Dmcq (talk) 02:36, 29 May 2011 (UTC)

It depends what you mean by "difference". In mathematics, a difference is the answer to a subtraction, so 3x minus 1x would give 2x as the "difference". Colloquially, the word "difference" is sometimes used informally to be a synonym of "quotient", so 3x divided by 1x gives an answer of 3 (i.e. 3x is three times as big as 1x). As Dmcq says above, we need to know more detail to be able to answer usefully. Dbfirs 08:01, 29 May 2011 (UTC)

Oh I see, thanks. I do wish people would make a little extra effort to explain themselves. It seems to be a question about the English language rather than mathematics. If one thing is three times another then would one say the difference between the two is two times or three times the smaller one? It is like those questions about percentages where they say one thing is 120% times as big as another and confuse everyone. And the answer is anybody's guess, if you don't know then the person saying it has simply talked words rather than communicated. Dmcq (talk) 11:05, 29 May 2011 (UTC)

The statement "X is 120% as big as Y" is unambiguous; it's the statement "X is 120% bigger than Y" that's the problem. The latter statement should mean that X is 220% as big as Y, but it is often used to mean that X is 120% as big as Y (which would properly be described by saying that X is 20% bigger than Y). See also A onefold decrease is quite enough, thank you, though I imagine there is a lot of room for argument in what the "proper" usage of some of these phrases should be. —Bkell (talk) 15:56, 29 May 2011 (UTC)

Bkell, another ambiguous type of expression is "the second most [adjective] [noun] after [noun]", for example, "the second largest planet after Jupiter", which might mean "Saturn" (the second largest planet) or "Uranus" (the third largest planet).

—Wavelength (talk) 16:20, 29 May 2011 (UTC)

Good point. Recently I read a sentence that said something like, "Human trafficking is the second largest illegal trade worldwide, after drugs and guns." That one really made me scratch my head. —Bkell (talk) 16:27, 29 May 2011 (UTC)

There are three kinds of people, those who can count and those who can't. Bo Jacoby (talk) 08:39, 1 June 2011 (UTC).

"Difference" normally means what you get by subtracting. Thus

$3x-1x=2x.\,$

The difference is 2x. Michael Hardy (talk) 23:12, 29 May 2011 (UTC)

... but only in Mathematics, and then only when mathematicians are using language precisely. Unfortunately, some people use "difference" to refer to a comparison factor, and even respectable organisations like the BBC sometimes say "3 times more" when they mean "3 times as much". This question really belongs on the language desk. Dbfirs 22:32, 30 May 2011 (UTC)

what's the relationship between 'formula' 'equation' 'function' in mathematical Perspective?

Is there exist a probability to show there relationship by using sets? For example(only my opinion): All functions are equations. All equations are formulas. ... So we can use sets to express there relations.

My question is: If we can express their relations by using sets, how should we arrange them? If we can't, how should we express them by using English?Nilman (talk) 09:28, 29 May 2011 (UTC)

An equation can be used to represent a function_(mathematics), but that doesn't mean there is some set inclusion between the classes. Consider the function which returns 1 for any rational number, and 0 for any irrational. What is the equation for that? Likewise, consider the equation a=b+c. What function is that? You could consider it a(b,c), a function of two variables, or a function of one variable, a(b) with one parameter c. There is no 1-1 (single, canonical) mapping between equations and functions. Does that help? SemanticMantis (talk) 14:27, 29 May 2011 (UTC)

(edit conflict) In standard terminology, "equation" refers to a proposition where the relation is equality, e.g. $1+2=3$. "Formula" is more-or-less synonymous with "equation", and is especially used to refer to an equation that expresses a value in terms of other, easily-computable values (e.g. quadratic formula). Functions are mathematical objects, some of which may be defined by equations. So, for example, $f(x)=3x^{2}$ is an equation or formula that describes or defines a function $f$. Set-theoretic definitions of function objects are given in the "Definition" section of our function article. So, it is not correct to say that, for example, "all functions are equations". (In fact, it is easy to demonstrate that there are an uncountably infinite number of functions that cannot be defined by any finite-length equation, but I digress.) Does that clear things up at all? « Aaron Rotenberg « Talk « 14:32, 29 May 2011 (UTC)

Thank you.Nilman (talk) 10:50, 30 May 2011 (UTC)