💡𝚂𝗆𝖺𝗋𝗍𝗆𝖺𝗇 𝙰𝗉𝗉𝗌📱

I really want to have a good discussion about this

says person who deleted their previous post when I proved how wrong it was 😂

it is not possible with your debate style

There’s no debate - the rules are in Maths textbooks, which you want to pretend don’t exist

You fail to understand the argument your opponent is making

You haven’t got one. That’s why you keep pretending Maths textbooks don’t exist

By divorcing each partial statement from its surrounding context

says person who deleted one of their posts to remove the context. 😂 The context is the rules of Maths, in case you needed to be reminded 😂

you are likely to change its meaning

Nope. I’m still talking about the rules of Maths 😂

You are not making a point of your own

Ok, so here you are admitting to comprehension problems. Which part did you not understand in addition and subtraction can be done in any order? 😂

You are simply stating facts, opinions, or misunderstandings as if they are self-evidently true

You left out backing it up with textbook screenshots and worked examples 😂

without knowing why you believe them to be true.

There’s no belief involved. It’s easy enough to prove it yourself by doing the Maths 😂

it’s very easy to state two contradictory things without realizing it

And yet I never have. Why do you think that is? 😂

“No they can’t. The rules are universal”

Which is correct

“It’s only a convention, not a rule, as just proven”

Which is also correct, and in no way contradicts the previous point, and I have no idea why you think it does! 😂 The first point is about the rules, and the second point is about conventions, which isn’t even the same thing

this also makes it hard for people to find the mistakes

That’s because I’m not making any 😂

I can see that you don’t fully understand what I mean by “operator precedence”

Says person who in their other post claimed “addition first” for -1+3+2 is -(1+3+2) = -6, and not +(3+2)-1=4 😂

If your opponent also used this debate style,

Which you don’t, given you have no evidence whatsoever to back up your points with 😂

ends up entirely divorced from the initial meaning

I’ve been on-point the whole time, and you keep trying to deflect from how wrong your statements are 😂

Please do not take these as insults

Well, obviously not, given I just proved they were all wrong 😂

allows you to understand why people know the brackets matter.

Except I’ve proven, repeatedly, that they don’t, and so now you’re trying to deflect from that (and deleted one of your posts to hide the evidence of how wrong you are) 😂

Some other pedantic notes you may find interesting

It’s hilarious that you added in this in afterwards, hoping I wouldn’t see it so you could claim the last word 😂

There is no “correct answer” to an expression without defining the order of operations on that expression

There is only one order of operations, defined in many Maths textbooks.

Addition, subtraction, etc. are mathematical necessities that must work the way they do

Hence the order of operations rules, found in Maths textbooks

But PE(MD)(AS) is something we made up

PEMDAS actually, and yes, it’s only a convention, not the rules themselves

there is no actual reason why that must be the operator precedence rule we use

That’s why it’s only a convention, and not a rule.

this is what causes issues with communicating about these things.

Nope, doesn’t cause any issues - the rules themselves are the same everywhere, and all of the different mnemonics all work

Your second example, -1+3+2=4, actually opens up an interesting can of worms

No it doesn’t

so subtraction is a-b

Just -b actually

negation is -c

Which is still subtraction, from 0, because every operation on the numberline starts from 0, we just don’t bother writing the zero (just like we don’t bother writing the + sign when the expression starts with an addition).

a two-argument definition of subtraction

Subtraction is unary operator, not binary. If you’re subtracting from another number, then that number has it’s own operator that it’s associated with (and might be an unwritten +), it’s not associated with the subtraction at all.

you can also define -1 as a single symbol

No you can’t. You can put it in Brackets to make it joined to the minus sign though, like in (-1)²=1, as opposed to -1²=-1

not as a negation operation followed by a positive one

The 1 can’t be positive if it follows a minus sign - it’s the rule of Left Associativity 😂

These distinctions are for the most part pedantic formalities

No, they’re just you spouting more wrong stuff 😂

you could argue that -1+3+2 evaluated with addition having a higher precedence than subtraction is -(1+3+2) = -6

No, you can’t. Giving addition a higher priority is +(3+2)-1=+5-1=4, as per Maths textbooks…

Isn’t that interesting?

No, all of it was wrong, again 😂

you’re just using (AS) without realizing it

as per the textbooks 🙄

Conversations around operator precedence can cause real differences in how expressions are evaluated

No they can’t. The rules are universal

you might not underatand it yourself

says someone about to prove that they don’t understand it… 😂

With (AS), 3-2+1 = (3-2)+1 = 1+1 = 2

Nope! With AS 3-2+1=+(3+1)-(2)=4-2=2

This is what you would expect

Yes, I expected you to not understand what AS meant 😂

since we do generally agree to evaluate addition and subtraction with the same precedence left-to-right

It’s only a convention, not a rule, as just proven

With SA, the evaluation is the same

No it isn’t. With SA 3-2+1=-(2)+(3+1)=-2+4=2

you get the same answer

Yep, because order doesn’t matter 🙄 AS and SA both give the same answer

No issue there for this expression

Or any expression

But with AS, 3-2+1 = 3-(2+1)

You just violated the rules and changed the sign of the 1 from a + to a minus. 🙄 -(2+1)=-2-1, not -2+1. Welcome to how you got a wrong answer when you wrongly added brackets to it and mixed the different signs together

So evaluating addition with higher precedence rather than equal precedence yields a different answer

No it doesn’t., as already proven. 3-2+1=+(3+1)-(2)=+4-2=2, same answer 🙄

They do, it’s grouping those operations to say that they have the same precedence

They don’t. It’s irrelevant that they have the same priority. MD and DM are both correct, and AS and SA are both correct. 2+3-1=4 is correct, -1+3+2=4 is correct.

Without them it implies you always do addition before subtraction, for example

And there’s absolutely nothing wrong with doing that, for example. You still always get the correct answer 🙄

PE(MD)(AS) Now just remember to account for those parentheses first

Those Brackets don’t matter. I don’t know why people insist it does