I am familiar on how limits work and such. For example, look at the following limit: $$\lim_{x\to 5^+} \frac{-x^2+5x}{5-x} = 5$$ It is saying that, as $x$ approaches $5$ from the right, the equation approaches $5$ as well, but will never be exactly equal to $5$
However, I began experimenting different limits on a TI-89 and I decided to try $$\lim_{x\to \infty^+} \frac{1}{x}$$ That is, the limit of $\frac{1}{x}$ as $x$ approaches $\infty$ from the right.
The calculator gave me an answer of $0$.
However, conceptually I do not see how you can approach $\infty$ from the right, as there isn't supposed to be anything bigger than $\infty$. How can this be possible? Or is this merely a calculator bug that was overlooked in its programming?
The comment made by YoTengoUnLCD is not exactly correct. From the definition of limits, $$ \lim_{x \to \inf} \frac{1}{x}=0 $$ means that, for each $\epsilon >0$, there exists N such that $$ \lvert\frac{1}{x}\rvert<\epsilon $$ whenever $x>N$. (Although, in practical terms, it would be wise to treat infinity vaguely as a really big number in many problems.) Also, since there can be no number that is greater than infinity, the notation $$ \lim_{x \to \inf^+} \frac{1}{x} $$ is meaningless. So why does your calculator observe the limit as $0$? My guess is that the TI calculator takes the limit without the plus sign (i.e. the limit side) first. I think that the calculator has some sort of loop that says (1)observe the limit without the limit side sign $\to$ (2)if the limit from (1) exist, then stop and display the result from (1); if not, continue to (3) $\to$ (3)take the limit $with$ the limit side sign. I think that the loop would've been designed this way because it would simplify lots of calculations. If the calculators made a loop that (1)evaluated the limit from the left, (2)evaluated the limit from the right, and (3) check whether both limits exist, that would've been taken slightly longer time. After all, many limit notations we evaluate aren't one-sided limits (more often than not, anyway).