Is this a contradiction on Wolfram Alpha?

2 points·teilo··5 comments

Consider the two following inputs to Wolfram Alpha:

10(0/0)

and:

x(y/y) where x=10,y=0

The result of the first, as expected, is indeterminate:

http://www.wolframalpha.com/input/?i=10(0/0)

But the second is 10:

http://www.wolframalpha.com/input/?i=x(y/y)+where+x+%3D+10,+y+%3D+0

Is this a bug?

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Definitely it is a bug in the Wolfram Alpha.

Mathematically the correct answer is "Indeterminate" but parsing the statement in a computer science world, both results are correct.

The statement "10(0/0)" requires no reduction of equation. The statement will translated into "10 * ( 0 / 0 )" but the statement "X(Y/Y)" it requires reduction of equation into "X" therefor all you need is the value of X.

Pragmatist engineers will say that y/y is always equal to 1, so x(y/y) will always equal x.

Mathematicians will say that such reasoning has been known to lead to contradictory conclusions, and the form (y/y) is always equal to 1, except when y=0, inwhich case it is indeterminate.

You need to choose which universe you live in, and how paranoid you have to be.

So Wolfram Alpha is erring on the side of the Engineers rather than the Mathematicians?

Links to those two queries:

http://www.wolframalpha.com/input/?i=10(0/0)

http://www.wolframalpha.com/input/?i=x(y/y)+where+x+%3D+10,+...

You put x(y/y) so if y is ever 0, it should be indeterminate, I believe. Both equations appear to equal the same thing which is indeterminate.

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