Message Boards Message Boards

GROUPS:

Why : and / symbol handled different in W|A? Both mean division.

Posted 26 days ago
229 Views
|
10 Replies
|
3 Total Likes
|

Why the results of these expressions are different?

https://www.wolframalpha.com/input/?i=48:2(9%2B3)

https://www.wolframalpha.com/input/?i=48%2F2(9%2B3)

It's 2 vs 288.

Both : and / symbols represent division which has one and only definition. Should be handled the same regarding commutativity, associativity and distributivity.

Attachment

Attachments:
10 Replies

I wonder why the different treatment within the same application. I think Wolfram|Alpha should detect such ambiguities and prompt the user for a disambiguation.

: is not universally used for division. In contemporary Hungarian, it is indeed standard. I was taught $a:b$ before $a/b$ in primary school. But in English, it is not. At the elementary level, ÷, and not : is used for division. Yes, math notation is specific to languages too. Think of it as decimal comma vs. decimal point.

: is often used for the concept of "ratios". This is how W|A is interpreting it here, and this is why the operator precedence is different.

To sum up: If you mean the arithmetic operation, use /. Use : only if you want to operate with ratios that are explicitly kept in ratio form. There is no numerical result for :, but you can have more than one term in the ratio, e.g. try 2 : 6 : 4. It will simplify to 1 : 3 : 2.

A marginally related note: The influence of computer languages seems to be slowly changing the standard math notation. I see $*$ used for multiplication more and more often, written in LaTeX. I often see people writing things like $a*\frac{b}{c}$ online. This use really makes me cringe, but maybe I am just old-fashioned. I am used to $*$ meaning convolution or some other uncommon (or even unspecified) mathematical operation in textbooks. I wonder when we will see the first textbook using $*$ for multiplication ...

The first case used : as ratio, and W|A made that explicit. So there is nothing unusual there. The second has also a matter of operator precedence: should the expression be 24/(2*(9+3)) or (24/2)*(9+4)? That the latter was used follows from what I believe is the most common convention, grouping operators of equal precedence left-to-right.

It is interesting to see how mathematical notation changes over time. Today, in English, we use decimal points (on the baseline), and we use a comma for digit groups. In Hungarian (and in many other European continental countries), we use a decimal comma, and a thin space for digit groups.

However, if I look at a Hungarian language encyclopaedia published in the 1920s, I see a centred decimal point, a comma for the thousands group and a baseline point for the million group.

enter image description here

The same encyclopaedia uses $\frac{a}{b}$ or $a:b$ for divison, but not $a/b$.

Posted 26 days ago

Thanks all for your answers. I now looked after the meaning of : symbol to clear it up and the situation is still interesting. Here's the definition on Wikipedia, and focus on the example on the right side: Definition of : symbol on Wikipedia

So it is right the same as / symbol's:

10:2=5 ≡≡≡ 10/2=5

WHICH MEANS:

48:2(9+3) ≡ 48/2(9+3)

WHICH MEANS that they must lead to the same result. So the question is now stronger than before: Why WolframAlpha handles them different?

You should read, carefully, what W|A and others have noted. The colon is being used as a ration, and this is a correct usage. That it is not your expected or preferred usage is not really relevant.

Moreover, there is the issue of operator symbol precedence. This seems to be getting ignored here. Yet it matters.

I think it is pointless to argue about what is the definition of a symbol. If you write your own book, you can make it whatever you want it to be. For as long as you are clear about it, it is still a good book.

W|A is clear about its interpretation.

So what is the problem then?

Also, how would you represent ratios if : is taken for division only?

This is a bit like arguing that either Fortran, C or Mathematica is "wrong" when they denote exponentiation by **, pow and ^ respectively. Yet all three work just fine, and all three can compute powers.

Posted 26 days ago

Szabolcs, the problem is that, math is a language and its scriptum has its own grammar. In other words: math symbols must have one and only definition.

Based on this, you must use math logic which also can not be altered because altering math logic is a fail;

  1. Nobody can alter a symbol's meaning, just like, e.g., you and even I must NOT define "nobody" as "everybody". Because nobody means nobody; this is the consensus about this notion.

  2. So, division is division with its own commutativity-associativity-distributivity configuration, and : symbol is division.

Describing it more math-ish:

  1. Division operation is not commutative, not associative, and is distributive.
  2. / symbol = division
  3. : symbol = division

AND WHEN we put an expression into WolframAlpha then we expect a credible result.

The point I was trying to get across:

  • Your expectation is culturally determined, thus there is no "correct" notation. There is no universal notation.
  • If you pay attention to W|A's output, there can be no confusion.

We are grateful to all participants for their contributions. We consider the issue to be resolved and comments starting to stray away from Wolfram Technology topics. This discussion thread is being closed to further comments. See: http://wolfr.am/READ-1ST

Group Abstract Group Abstract