Symbols are visual shorthand used to represent something else. Other common terms are signs and ideographs (or ideograms). I have a couple books about symbols and there are thousands of examples.
In essence, these marks are used to represent an idea or concept - sometimes vaguely and sometimes quite precisely.
For example, this means recycling ♲ and this means recycling a certain type of plastic ♴
☃ it's clear that this means a snowman. That's a cheerful but irrelevant symbol.
☹ you might be slightly down when you use this, but it's not as serious as using this! ☠
In mathematics, we use lots of symbols, both to save space, and to convey specific meanings that are inconvenient to express in words.
Here are a few for you to review:
+ - × ÷ ± = Arithmetic, easy right?
How about these modified equal signs?
≇ Neither approximately nor exactly equal to
≈ Almost or approximately equal to
≤ Less than or equal to
≥ More than or equal to
Still with me? Let's try a few more
⋚ This must mean everything because its title is Less-Than, Equal-To or Greater-Than
⩐ This is a Closed Union with Serifs and Smash Product. I have no idea what that means!
⨋ Summation with Integral
It goes on and on. Every technical field is filled with symbols.
��__ This invisible musical symbol is called a clef. It appears only if your software supports it. My desktop displays this symbol but the browsers don't!
(This introduces a concept called FONTS and we don't want to get started on that slippery slope!!!)
Symbols are useful in everyday life too.
⌘ This means a place of interest, and you can get information about it here i
∞ This means infinity (and literally there is no end to the symbols you can create)
. In American we call this a period. The English call it a FULL STOP and we might as well make one now