Missing multiplication symbol: Difference between revisions

From Why start at x, y, z
No edit summary
No edit summary
 
(3 intermediate revisions by 2 users not shown)
Line 7: Line 7:
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>
Line 13: Line 13:
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 \(\frac{2}{3x}\)
Line 20: Line 20:


\[ ab^2 = a \times (b^2) \]
\[ ab^2 = a \times (b^2) \]
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

  1. Tweet by Christian Lawson-Perfect
  2. Twitter thread by Christian Lawson-Perfect
  3. Igor Pak, How to Write a Clear Math Paper: Some 21st Century Tips
  4. The Times, They Are A-Changin', Jim Simons, Mathematics in School, November 2020.