How would I represent the number, i, that is one increment larger than $x$, where an increment is infinitely small.
For example, if $s \in (1,2)$, $i$ would be the smallest number $s$ can take on if $x=1$. I thought about making it $i= x+ (\lim_{n\to\infty} \frac{1}{n})$ but this evaluates to $x$. How would I represent this number $i$ for a given $x$?
I could represent it as $i=\text{min}(s)$ for $s \in (x,\infty)$ but this seems messy. I'm looking for a cleaner way to write this if possible
On
i+1/∞
Why?
Short: Infinity is a deferred loop stop.
Infinity (∞) is a loop in an information processor (brain, computer),
that does never stop, like while True: ....
Since the looping never stops it never gets into existence as such.
This kind of ∞ therefore does not exist.
Consequently ∞ is an infinite loop, where the stop is deferred to later. The number of actual loops is thus defined by the need of the context.
The real numbers have a double infinite loop: dense (arbitrarily precise) and infinite (arbitrarily large).
√2,... and also 1, 2,... ∈ℝ do not exist other than "depending on the situation we want this or that precision". In the same sense ∞ means "depending on the situation we want a number large enough".
So i+1/∞ means stop when close enough to i from above, where the reader can decide what enough means in a situation.
Based on the reading from Player3236's comment, I understand that this is not possible and more importantly why this is not possible. examples to understand why for any future readers