>>12284637There is no number between .99... and 1. They are the exact same number. They do the same things when manipulated. They are the same number. Using a physical model like this tells us nothing, you can't have an infinitely large body of water. Also, idk why nobody pointed this out, your equation is wrong. A ml of water is a gram, so your initial math is correct, however, a gram of salt is not a milliliter of volume, but this isnt the priblem with what you said haha.
Would it help you to visualise that no matter how you sampled it, you would never get the salt? Like, if you had a house to get to, but you had to drive across an infinite plane to it, it literally could not be anywhere. Any placement of the house a distance away from you would negate its infinite distance from you.
In the same way, a limit is just saying what has to be. If I have the parabola y = x^2 and the line y =0, and some equation that is less than or equal to y = x^2 and greater than or equal than y = 0, can you see how it would have to be zero at zero? That is the only possible value that satisfies this relationship. With a limit, we can ask a similar question of any equation. When we approach x value, what, if anything do we approach? For .99... the number we approach is 1, at any possible finite sequence, it is not 1, qbsolutely, but at the end of infinity, the only value possible for this value is 1. Any .99999 would have already have been reached. The value when all .99999s have been gotten rid of is 1. It is indistinguishable from this infinite set of .99s.
With your hypothetical, the salt can not take up any amount of volume relative to this infinity. If it did so, it wouldnt be an infinity. There isnt a bound to point at and say, we are this % of it. Anon, imagine I have a finitearrangement of 1s and 0s, say 01. Surely, you would not say this arrangement is some percentage of the 0s and 1s possible? There is no control on how many patterns there can be. They are infinite.
