Evaluate 1/3 + 1/3+ 1/3 with infinitesimals

Question

anonymous · Answer

1?

anonymous · Answer

.9999999999999999999999999999999999999999999999999999999999999999999...

agreene · Answer

$$\lim_{x \rightarrow 3} (x^{-1}) + lim_{x \rightarrow 3} (x^{-1}) +lim_{x \rightarrow 3} (x^{-1}) = 0.9999999... = 1$$

anonymous · Answer

i'm wondering how'd you write it in infinitesimal form... i think it'd be like infty/infty +1/infty

agreene · Answer

Well, an infinitesimal is something infinitely small (or sufficiently small). Back in the 1600s they would just pick a super small number to approximate it.

0.33333333333333333333333333333333333333333333333333333333333333 = 1/3 for example

anonymous · Answer

yeah or in otherwords $$\frac{1}{\infty}$$

anonymous · Answer

i'm wondering how'd you write .99999 in infinitesimal...like this?

$$\frac{\infty}{\infty+\frac{1}{\infty}}$$

agreene · Answer

except...
$$\frac{1}{\infty} = 0$$

you can write .9999 as an infinitesimal, either just like that or some combination of recursive limits if you really want to.

anonymous · Answer

but 1/infty in infinitesimals i thought meant that 1/infty is not zero just extremely small to the point that they just ruled out 1/infty and said it was 0