# Missing multiplication symbol

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