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From https://www.gnu.org/software/bash/manual/html_node/Tilde-Expansion.html

If a word begins with an unquoted tilde character (‘~’), all of the characters up to the first unquoted slash (or all characters, if there is no unquoted slash) are considered a tilde-prefix.

From my experience or intuition (I am not sure which), "up to" means the following is included. But I am not sure if that is correct when reading the quote. So generally speaking does "up to" mean the following is included or not?

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Up to does not include the slash. In your specific bash example:

~ gives you: $HOME
~/hello gives you: $HOME/hello

Only the "~" is substituted by "$HOME", the rest of the string is then parsed. The "/" is usually used as a delimiter and so is not included as part of any substitution string unless specifically escaped.

Usually up to and including the slash would mean "~/", and so up to means up to, but not including. If you walk up to a wall, you do not end up in the wall, you are just next to it...

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