Why am I only just now realising that:
15 - 5 - 1 = 9
while:
15 - (5 - 1) = 11
When an expression has addition/subtraction as well as multiplication/division, I always understood the need for brackets around the +/- to prioritise them (#BODMAS). I just never realised it also changed the value of expressions that *only* use subtraction...
@ConditionalCoder
The phrase you may be looking for is "non-associative".
Also, note the difference between the binary operation of subtraction and the unary property of negativeness for which we use same symbol.
(+15) - (+5) - (+1) = (+9)
(+15) + (-5) + (-1) = (+9)
(+15) - ( (+5) - (+1) ) = (+11)
(+15) - ( (+5) + (-1) ) = (+11)
Another fun example of non-associativity is in exponentiation. :-)
https://en.wikipedia.org/wiki/Associative_property
#maths #arithmetic #algebra #mathematics