RE: simple maths or simple minds?
April 5, 2021 at 9:12 am
(This post was last modified: April 5, 2021 at 9:15 am by polymath257.)
(April 5, 2021 at 1:22 am)░I░G░N░O░R░A░M░U░S ░ Wrote: 50+50-25x0+2+2=?
It's ridiculous how many get this wrong on the net.
It's basically a sad reflection of the education system of the west ...
Maths flew us to Mars
No maths flew us into buildings...
At least part of the difficulty is that the order of operations is a *convention*. We have decided that multiplication takes priority over addition and subtraction. But there is nothing other than our convention to dictate this. Hence, those who don't know or don't remember the convention cannot reconstruct it just from the mathematical operations themselves.
This is why parentheses are used in mathematics: to resolve such ambiguities. But, that is not the only way to do this. We could use reverse Polish notation instead of the conventional one and such ambiguities are eliminated without parentheses.
So, in the above expression, here are the two RPN possibilities:
50 50 + 25 - 0 x 2 + 2 +
or
50 50 + 25 0 x - 2 + 2 +
The first has a value of 4 and the second has a value of 104.
(April 5, 2021 at 1:26 am)Eleven Wrote: Does it have to do with the stupid FOIL rule? It's like math decided to team up with a trickster to intentionally trip you up. It's really dumb.
It's more that mathematicians have found all the strange alternatives and have figured out ways to reduce the ambiguity. FOIL, for example, follows from the properties of addition and multiplication. I actually find FOIL to be a very *bad* way to explain what is going on because it fails once you have more than two terms of two terms multiplied together.
