A Simple Calculation
Re: A Simple Calculation
Poodle wrote:Point taken, xouper. But I think my point about typographic interpretation still stands. I do not know what convention was used, if any, in the expression 6 / 2 (2+1) = x.
There is a disagreement between mathematical and typographical interpretation which I think is valid. I cannot know  and nor can you  if a strict interpretation has been followed. There is, surely, a better way to express it than the one given  the whole point of the post, I should imagine.
As a professional editor, I would have asked the originator to express himself more clearly. But then I'm a pedant  that's what editors do.
I'm a pedant too — that's what programmers do. Your observations are essentially the same point I tried to make in my first post. It seems djembeweaver agrees, but I don't speak for him.
Speaking of ambiguities, I don't know what you mean by "strict" in your comment. There are only two possible interpretations and (putting on my mathematician hat) I do not know which one is considered the "strict" interpretation.
Poodle wrote:There is a disagreement between mathematical and typographical interpretation which I think is valid. I cannot know  and nor can you  if a strict interpretation has been followed.
If we interpret "strict" to mean "default", then yes I can know. As I explained earlier, google calculator had no problem interpreting the formula as written. Google calculator follows the same rules of interpretation as most mathematicians and programmers.
The ambiguity disappears when one knows which of two sets of rules should be applied. The question then is, if left unstated, which rules do the professionals expect to be used? If unstated, is there a default position? I think google calculator gives us that answer.
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Re: A Simple Calculation
xouper wrote:My preference as a professional programmer is not to rely on the compiler's precedence rules. It is safer to add explicit parentheses to force the precedence I want. Then there can be no ambiguity and it is clear to anyone reading the code what I had in mind.
This is my preference as well.
Either specify (6/2)*(2+1) or 6/(2*(2+1)) to make sure you get the result you intended.
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Re: A Simple Calculation
xouper wrote:djembeweaver wrote:xouper wrote:Here's a simpler example of the two notations:
1/3
means the exact same thing as
1
—
3
The first is inline notation and the second notation uses a fraction bar. They represent the same exact mathematical operation and it is indeed valid to refer to the inline notation as a fraction. When I say 1/3, it is not unreasonable to say the denominator is 3, even though I used the inline notation. A denominator is just another name for a divisor.
Hmmm...really? I'm not convinced. Just because they are functionally the same, that doesn't mean they are identical (does it?).
That's an interesting question. In mathspeak, that seems to be saying that in determining identity, an equivalent functionality is necessary but not sufficient. You may be right, which could be demonstrated with a counter example, if you have one.
However, I claim they are identical because they are merely two names for the same thing, not just because they function the same.
http://www.mathgoodies.com/glossary/term.asp?term=fraction%20bar
http://mathforum.org/library/drmath/view/58321.html
https://en.wikipedia.org/wiki/Algebraic_fraction
https://en.wikipedia.org/wiki/Fraction_%28mathematics%29wikipedia wrote:Other uses for fractions are to represent ratios and to represent division.[1] Thus the fraction 3/4 is also used to represent the ratio 3:4 (the ratio of the part to the whole) and the division 3 ÷ 4 (three divided by four).
As you saw in that video he shows three inline names (symbols) for division, the slash, the obelus, and the colon. Not only do they function the same, they are the same because they are merely different names for the same function. In addition to those three "inline" names (notations), the fraction bar (sometimes also called a vinculum) is yet another name for division, although it is not an "inline" notation.
Example:
(x^{2}  1)
———
(x 1)
means to divide (x^{2}  1) by (x 1).
How is that not exactly identical to (x^{2}  1) / (x 1)?
Another example of multiple names for the same thing:
x ^ (1/2)
x ** (1/2)
x^{1/2}
√x
sqrt(x)
They are all different names for the same thing, the "square root of x". Not only do they function the same , they are the same. They are indeed identical. I argue similarly that the fraction bar is just another name for division.
Does this answer your question, or have I misunderstood your point?
According to the guy in the video I posted the slash symbol is not a fraction bar, and confusing it with a fraction bar is one common mistake in interpreting such problems.
I think the best demonstration that they are not equivalent is the problem itself, since if a fraction bar was used instead of a slash then which interpretation is intended would be implied in the way the expression is written.
Thus a single expression using inline notation devolves into two possible expressions using fraction notation. Surely this proves that they are, on some level at least, not equivalent.
Re: A Simple Calculation
djembeweaver wrote:According to the guy in the video I posted the slash symbol is not a fraction bar, and confusing it with a fraction bar is one common mistake in interpreting such problems.
He is mistaken. Perhaps he did not explain sufficiently what kind of "common mistake" he thinks it is.
djembeweaver wrote:I think the best demonstration that they are not equivalent is the problem itself, since if a fraction bar was used instead of a slash then which interpretation is intended would be implied in the way the expression is written.
I see what you are saying, but I disagree with your conclusion. Using a notation that removes the ambiguity does not mean that you cannot use a fraction bar to express a division. It merely means that one notation is less ambiguous than the other.
djembeweaver wrote:Thus a single expression using inline notation devolves into two possible expressions using fraction notation. Surely this proves that they are, on some level at least, not equivalent.
The only thing it proves is that the inline notation can be misused in a way to introduce ambiguity. It does not prove that a fraction bar is not equivalent to division.
Using the inline notation the way you did also devolves into two possible expressions depending on which precedence rules you use. The choice of which precedence rules to use does not make the inline notation any less equivalent to the fraction bar notation. By that I mean, the fraction bar equation can be written to exactly match whatever precedence rules you wish to impose on the inline version. This proves the operations specified by the notations are indeed equivalent.
Since you seem to be saying they are not equivalent, then please show how the inline division notation gives a different result than using the fraction bar notation when using the same precedence rules. Use any example you like, you are not limited to the example in your opening post.
I claim you can translate back and forth between the two notations and the result will always be the same, assuming you use the same precedence rules.