it contradicts the second half of what you said. If the multiplication by juxtaposition implied a group then 2(2+2) is shorthand for (2*(2+2)).
That's my point. There is no shorthand with parentheses here. The only shorthands in math don't change precedence, i.e. 2(2+2) is shorthand for 2*(2+2) and nothing else.
"My phone says it so it's true." This generation, I swear.
My decades of working with math is why I know it is true. I only mentioned the phone to prove it to those of you who are so confident about being wrong. The developers of those calculator apps all have a better understanding of operator precedence than you do, hence why they all give the same (and correct) answer. And I would bet that I'm older than you.
That's my point. There is no shorthand with parentheses here. The only shorthands in math don't change precedence, i.e. 2(2+2) is shorthand for 2*(2+2) and nothing else.
My decades of working with math is why I know it is true. I only mentioned the phone to prove it to those of you who are so confident about being wrong. The developers of those calculator apps all have a better understanding of operator precedence than you do, hence why they all give the same (and correct) answer. And I would bet that I'm older than you.