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/ <- It leans to the right (or forward for left-to-right readers).
This character is a "slash", or "front slash, or "forward slash". The Brits call it "stroke", as in "27 b stroke 6".
On the QWERTY computer keyboard, it shares a key with and is underneath the question mark '?'
It is used sometimes in markup (editing words, music, probably elsewhere) and long ago was used in lieu of a period in punctuation. Technically it is named "solidus" or "virgule", but nobody calls it that. It's a slash.
It is used in mathematics as the fraction/division symbol.
It is used in lieu of "and" and "or", such as in the sentence above ("fraction/division"). It is also use to separate the words "and" and "or", when you mean "and and or" or "and or or" like so: "and/or", which is pronounced "and or".
It is the path separator in Unix (and Unix-like OSes) and in Internet URLs. A backslash is not used in place of a slash and vice versa, although on Windows OSes, your browser might accept backslashes as if they were valid, and it rewrites a backslash as a slash when actually sending the URL string to the remote server. This wrongslash-accepting behavior is a disservice to users, who then think they got it right. The use of the slash in Internet URLs is not merely coincidental to its use on Unix systems, as the Internet we know today was built on Unix and Unix-like systems. Microsoft's increased presence in the server space does not change this; backslash in this context is still wrong. The RFCs that describe and define the standards used on the internet always use the slash (/) character for these purposes. Even Microsoft OSes as old as XP accept the slash (/) as path delimiter, following suit with the rest of the world, likely due to the integration of IE and the file explorer.
The slash "/" should always be used when separating items whether it be parts of a URI (file path, URL) or a written string, or numbers to be divided.
\ <- It leans to the left - backward for left-and-right readers.
That character is a "backslash". I suppose the Brits might call it "backstroke", but I doubt it. Allegedly it is also known as the "hack", "whack", or "backwhack", but I've never heard anyone say this.
It shares a key with and is underneath the pipe ('|') character on a QWERTY computer keyboard.
It is used in mathematics for the relative complement of two sets.
It is commonly used as an escape character in programming/scripting languages, to denote a special character is to be taken literally, or to imbue a non-special-character with a special interpretation. Among the nerds who use it this way, it is sometimes called a "whack".
It is also used for line continuation, such that the newline immediately after it is understood to only be for ease of human reading, and that consecutive lines should be considered continuous.
It is the DOS/Windows path separator. It is used in UNC paths (such as WINS and CIFS shares), like \\HOSTNAME\sharename. This is the mirror image of the slash ("/") used in Unix and on the Internet. I suppose it is not surprising then that Microsoft got this backward, too, when deciding to use the backslash for the division operator in Visual Basic, contrary to, well, everything else. Microsoft's presence in the home and office computing space did not change the fact that nobody wants to use it this way, and in later languages such as C#, they got it right. Forward slash is still correct. The backslash appears in Internet RFCs, only for the purposes of denoting escape or line continuation.
The backslash "\" should be used when, well, in DOS. And when programming Visual Basic, but I don't believe people still do that.
This is a slash: /
It is used everywhere. Don't call it a backslash.
This is a backslash: \
If I had to explain that to you, you probably don't need it.