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

Posted 3 months ago
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 Why the results of these expressions are different?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. Attachments:
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Posted 3 months ago
 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.
Posted 3 months ago
 : 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 ...
Posted 3 months ago
 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.
Posted 3 months ago
 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.The same encyclopaedia uses $\frac{a}{b}$ or $a:b$ for divison, but not $a/b$.
Posted 3 months 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: 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?
Posted 3 months ago
 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.
Posted 3 months ago
 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.