Missing multiplication symbol: Difference between revisions
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But sometimes it's not as clear: | But sometimes it's not as clear: | ||
Does \( a(b+1) = a \times (b+1)\), or is \(a\) a function? | Does \( a(b+1) = a \times (b+1)\), or is \(a\) a function?<ref>[https://twitter.com/christianp/status/798843905231888385 Tweet by Christian Lawson-Perfect]</ref> | ||
When writing a division on one line, does an implied multiplication bind more tightly than an explicit one?<ref>[https://twitter.com/christianp/status/1320650593241866241 Twitter thread by Christian Lawson-Perfect]</ref> | When writing a division on one line, does an implied multiplication bind more tightly than an explicit one?<ref>[https://twitter.com/christianp/status/1320650593241866241 Twitter thread by Christian Lawson-Perfect]</ref> | ||
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Is \(a/bc\) equivalent to \(\frac{a}{bc}\) or \(\frac{a}{b}c\)? | Is \(a/bc\) equivalent to \(\frac{a}{bc}\) or \(\frac{a}{b}c\)? | ||
There seems to be an unwritten rule "juxtaposition is stickier". | There seems to be an unwritten rule "juxtaposition is stickier". (See [[Juxtaposition means combine in the obvious way]]) | ||
But that might not apply when there are numbers involved: almost everyone would interpret \(2/3x\) as \(\frac{2}{3}x\) instead of \(\frac{2}{3x}\) | But that might not apply when there are numbers involved: almost everyone would interpret \(2/3x\) as \(\frac{2}{3}x\) instead of \(\frac{2}{3x}\) | ||
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\[ ab^2 = a \times (b^2) \] | \[ ab^2 = a \times (b^2) \] | ||
Sometimes the ambiguity comes from mistaking a function for an operation: | |||
\[ (a+b) \Phi (a+b)\] | |||
which can be viewed as either \( (a+b)\cdot \Phi(a+b)\), or \(\Phi\) as binary addition-like operation, similar to \( (a+b)\oplus (a+b)\).<ref>Igor Pak, [https://scholarship.claremont.edu/jhm/vol8/iss1/14/ How to Write a Clear Math Paper: Some 21st Century Tips]</ref> | |||
Jim Simons reckons we should give up on implicit multiplicatoin altogether.<ref>The Times, They Are A-Changin', Jim Simons, Mathematics in School, November 2020.</ref> | |||
==References== | ==References== | ||
<references/> | <references/> | ||
Latest revision as of 09:18, 14 September 2021
It's common to omit a multiplication symbol:
\(ab = a \times b\)
But sometimes it's not as clear:
Does \( a(b+1) = a \times (b+1)\), or is \(a\) a function?[1]
When writing a division on one line, does an implied multiplication bind more tightly than an explicit one?[2]
Is \(a/bc\) equivalent to \(\frac{a}{bc}\) or \(\frac{a}{b}c\)?
There seems to be an unwritten rule "juxtaposition is stickier". (See Juxtaposition means combine in the obvious way)
But that might not apply when there are numbers involved: almost everyone would interpret \(2/3x\) as \(\frac{2}{3}x\) instead of \(\frac{2}{3x}\)
The "juxtaposition is stickier" rule only seems to break ties, not override the normal order of operations:
\[ ab^2 = a \times (b^2) \]
Sometimes the ambiguity comes from mistaking a function for an operation:
\[ (a+b) \Phi (a+b)\]
which can be viewed as either \( (a+b)\cdot \Phi(a+b)\), or \(\Phi\) as binary addition-like operation, similar to \( (a+b)\oplus (a+b)\).[3]
Jim Simons reckons we should give up on implicit multiplicatoin altogether.[4]
References
- ↑ Tweet by Christian Lawson-Perfect
- ↑ Twitter thread by Christian Lawson-Perfect
- ↑ Igor Pak, How to Write a Clear Math Paper: Some 21st Century Tips
- ↑ The Times, They Are A-Changin', Jim Simons, Mathematics in School, November 2020.
