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In the 16th century, the mathematician[br]Robert Recorde

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wrote a book called [br]"The Whetstone of Witte"

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to teach English students algebra.

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But he was getting tired of writing[br]the words "is equal to" over and over.

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His solution?

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He replaced those words with[br]two parallel horizontal line segments

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because the way he saw it,[br]no two things can be more equal.

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Could he have used four line segments[br]instead of two?

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Of course.

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Could he have used vertical line segments?

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In fact, some people did.

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There's no reason why the equals sign[br]had to look the way it does today.

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At some point, it just caught on,[br]sort of like a meme.

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More and more mathematicians[br]began to use it,

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and eventually, [br]it became a standard symbol for equality.

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Math is full of symbols.

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Lines,

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dots,

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arrows,

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English letters,

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Greek letters,

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superscripts,

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subscripts.

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It can look like an illegible jumble.

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It's normal to find this wealth[br]of symbols a little intimidating

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and to wonder where they all came from.

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Sometimes, as Recorde himself[br]noted about his equals sign,

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there's an apt conformity[br]between the symbol and what it represents.

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Another example of that [br]is the plus sign for addition,

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which originated from a condensing[br]of the Latin word et meaning and.

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Sometimes, however, the choice of symbol[br]is more arbitrary,

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such as when a mathematician[br]named Christian Kramp

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introduced the exclamation mark[br]for factorials

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just because he needed a shorthand[br]for expressions like this.

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In fact, all of these symbols [br]were invented or adopted

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by mathematicians who wanted[br]to avoid repeating themselves

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or having to use a lot of words[br]to write out mathematical ideas.

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Many of the symbols used[br]in mathematics are letters,

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usually from the Latin alphabet[br]or Greek.

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Characters are often found[br]representing quantities that are unknown,

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and the relationships between variables.

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They also stand in for specific numbers[br]that show up frequently

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but would be cumbersome or impossible[br]to fully write out in decimal form.

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Sets of numbers and whole equations[br]can be represented with letters, too.

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Other symbols are used [br]to represent operations.

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Some of these are especially valuable[br]as shorthand

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because they condense repeated operations[br]into a single expression.

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The repeated addition of the same number[br]is abbreviated with a multiplication sign

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so it doesn't take up more space[br]than it has to.

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A number multiplied by itself[br]is indicated with an exponent

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that tells you how many times[br]to repeat the operation.

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And a long string of sequential terms[br]added together

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is collapsed into a capital sigma.

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These symbols shorten[br]lengthy calculations to smaller terms

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that are much easier to manipulate.

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Symbols can also provide [br]succinct instructions

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about how to perform calculations.

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Consider the following set[br]of operations on a number.

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Take some number that you're thinking of,

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multiply it by two,

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subtract one from the result,

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multiply the result of that by itself,

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divide the result of that by three,

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and then add one to get the final output.

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Without our symbols and conventions,[br]we'd be faced with this block of text.

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With them, we have a compact,[br]elegant expression.

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Sometimes, as with equals,

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these symbols communicate meaning[br]through form.

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Many, however, are arbitrary.

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Understanding them is a matter[br]of memorizing what they mean

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and applying them in different contexts[br]until they stick, as with any language.

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If we were to encounter[br]an alien civilization,

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they'd probably have a totally[br]different set of symbols.

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But if they think anything like us,[br]they'd probably have symbols.

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And their symbols may even correspond[br]directly to ours.

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They'd have their own multiplication sign,

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symbol for pi,

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and, of course, equals.