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I use the following commands to change directory and it generally works fine.

[max@localhost max]$ cd /
[max@localhost /]$ cd /home/max/
[max@localhost max]$ pwd

But today, by mistake, I entered two // instead of one / and to my surprise, it works as well. So, I tried with various examples and all of them works just fine without giving any sort of an error.

[max@localhost /]$ cd /home///////////////max/////////////////////
[max@localhost max]$ pwd
[max@localhost max]$ cd /
[max@localhost /]$ cd /////////////////home/max///////////
[max@localhost max]$ pwd

What does these forward slashes mean (/ and ///////) and what do they do and represent?

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It's defined by IEEE standards:

A pathname may optionally contain one or more trailing slashes. Multiple successive slashes are considered to be the same as one slash.

There is actually a similar question and the solution is described there: How Linux handles multiple path separators.

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It simplifies combining paths by allowing you to avoid testing for leading or trailing slashes. You can just do path1 + "/" + path2 and it will work whether or not path1 has a trailing slash and/or path2 has a leading slash. – David Schwartz Aug 9 '12 at 13:24

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