# limit of infinity

i'm wondering is this valid?

$$\lim _{ x\rightarrow \infty }{ { (1+\frac { 1 }{ x } ) }^{ x }\quad =\quad { (1\frac { 1 }{ x } ) }^{ x }\quad =\quad ({ \frac { 1(x)+1 }{ x } ) }^{ x }\quad =\quad ({ \frac { x+1 }{ x } ) }^{ x }\quad }$$ and since $$\infty +1$$ does not make much of a difference so is still $$\infty$$ then $${ (\frac { x }{ x } ) }^{ x }\quad =\quad 1\quad$$ if we treat $$\infty$$ like a number.

therfore $$\quad \lim _{ x\rightarrow \infty }{ { (1+\frac { 1 }{ x } ) }^{ x }\quad =\quad 1\quad }$$

Note by Shufay Ung
4 years, 2 months ago

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You can't treat infinity like a number that's where the fallacy begins.

- 4 years, 2 months ago