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all i write is in R U {infinite}

i understood that inf-inf is an indeterminate form, i don't understand why inf+inf is not. for example, doing all possible steps:

[tex]inf+inf = \frac{n}{0}+\frac{n}{0} = \frac{n*\frac{0*0}{0} + n*\frac{0*0}{0}}{0*0} = indeterminate[/tex]

probably what i wrote is a non sense but can i have a proof that inf+inf=inf?

i understood that inf-inf is an indeterminate form, i don't understand why inf+inf is not. for example, doing all possible steps:

[tex]inf+inf = \frac{n}{0}+\frac{n}{0} = \frac{n*\frac{0*0}{0} + n*\frac{0*0}{0}}{0*0} = indeterminate[/tex]

probably what i wrote is a non sense but can i have a proof that inf+inf=inf?

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