I don't really understand why it hasn't been numerically added into modern math. I mean, we make all kinds of properties for zero, but we can't make properties for infinity? It gets messy from time to time, but we could define everything strictly so that it still works algebraically. 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."