I usually run the installers in bottles if it is a repack, then you can add the installed program to steam and make it look nice with steamgriddb. bottles lets you run just exe as well. if you name the game in steam to the steam id #, you can even get the official and community controller layouts

Correct, subtraction and division are not associative. However, what is subtraction if not adding the opposite of a number? Or division if not multiplying the inverse? And addition and multiplication are associative.

2-2-2 can be written as 2 + (-2) + (-2) which would equal -2 no matter if you solve left to right, or right to left.

In your example with the formula from right to left, distributing the negative sign reveals that the base equation was changed, so it makes sense that you saw a different answer.

2 - (2 - 2) = 2 + ((-2) + 2) = 2

I’ve always heard it that way too but I think it is for consistency with students, imo Logically, if you are looking at division = multiplying by inverse and subtraction = adding the negative, you should be able to do it both ways. Addition and multiplication are both associative, so we can do 1+2+3 = (1+2)+3 = 1+(2+3) and get the same answer.

Not quite, pemdas can go either from the left or right (as long as you are consistent) and division is the same priority as multiplication because dividing by something is equal to multiplying by the inverse of that thing… same as subtraction being just addition but you flip the sign.

8×1/2=8/2 1-1=1+(-1)

The result is 16 if you rewrite the problem with this in mind: 8÷2(2+2)=8×(1/2)×(2+2)

The problem with this is that the division symbol is not an accurate representation of the intended meaning. Division is usually written in fractions which has an implied set of parenthesis, and is the same priority as multiplication. This is because dividing by a number is the same as multiplying by the inverse, same as subtracting is adding the negative of a number.

8/2(2+2) could be rewritten as 8×1/2×(2+2) or (8×(2+2))/2 which both resolve into 16.

Just curious how you came up with 7%? I was always taught to expect the yearly return to be 4%

if you aren’t in your commute for 45 minutes, have you considered keeping an electric mug warmer at your desk? It usually doesn’t take up much space and it needs a small plug in

The best way I’ve been able to explain it is to put it in terms of email domains. If I am on gmail, and I can still interact with someone using outlook. But instead of email, it is essentially reddit, youtube, etc.