It’s not logic, it’s that what it means. 2*4 literally means 2+2+2+2. Just like 8/2 means how many times you can add 2 to itself until you get 8.
That’s what it means.
So why use braces? Because in more advanced maths you have more complex expressions that can’t be express in just multiplication which often occur in algebra or beyond.
For example what does 2 * ( a + 3) actually mean? Like why do we need to do the addition first. Its because we don’t know how many times we need to repeat the addition until we know what a means.
Let’s say a are points on an axis, and at some point it is worth three the. At that moment that expression is 2 * (3 +3) = 2 * 6 which is equal to 2+2+2+2+2
But in the next moment a might be 1
Right?
What’s arbitrary are the labels on the rules. The rules themselves aren’t arbitrary.
Multiplication is a notation which means add some number by itself a number of times.
5 x 3 = 5 +5 + 5
2 * 4 = 2 + 2 + 2 +2
So when you see some like 2 + 4 * 2 it literally means. 2+4+4
By that logic it could just as well be 2 + 4 * 2 = (2 + 4) + (2 + 4) = 12. You still need to know to multiply first, or it’s arbitrary
Order of operations proof - simple version
It’s not logic, it’s that what it means. 2*4 literally means 2+2+2+2. Just like 8/2 means how many times you can add 2 to itself until you get 8.
That’s what it means.
So why use braces? Because in more advanced maths you have more complex expressions that can’t be express in just multiplication which often occur in algebra or beyond.
For example what does 2 * ( a + 3) actually mean? Like why do we need to do the addition first. Its because we don’t know how many times we need to repeat the addition until we know what a means.
Let’s say a are points on an axis, and at some point it is worth three the. At that moment that expression is 2 * (3 +3) = 2 * 6 which is equal to 2+2+2+2+2
But in the next moment a might be 1
Right?
What’s arbitrary are the labels on the rules. The rules themselves aren’t arbitrary.