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Example: (quoted from http://mathforum.org/dr.math/faq/faq.divideby0.html)

5/0 = [tex]\infty[/tex]

5 = 0*[tex]\infty[/tex]

Multiplicative property of 0.

5=0

WRONG!

If we defined [tex]\infty[/tex] numerically:

5/0 = 1/0

5 = 0/0

We then, could define 0/0 as truly undefined, or all real numbers, or some other name. I don't think we need to classify something as undefined, or anything for that matter, unless it is 0/0, 0^0, [tex]\infty^\infty[/tex] etc.

As for infinity, it should be implemented carefully into our modern math.

Now it's time for you to post "Reasons why infinity hasn't been implemented into modern math."