‘If a+b equals b+a, why is 1/a+b different from 1/b+a?’
Because they’re not identically equal 🙄 Welcome to you almost getting the point
ab means a*b
means, isn’t equal
That’s why 1/ab=1/(a*b)
Nope, it’s because ab==(axb) <== note the brackets duuuhhh!!! 😂
But we could just as easily say 1/ab = (1/a)*b
No you can’t! 😂
because that distinction is only convention
Nope! An actual rule, as found not only in Maths textbooks (see above), but in all textbooks - Physics, Engineering, Chemistry, etc. - they all obey ab==(axb)
None of which excuses your horseshit belief that a(b)2
Yes we could, because it’s a theoretical different notation. Mathematics itself does not break down, if you have to put add explicit brackets to 1/(ab).
Mathematics does break down when you insist a(b)2 gets an a2 term, for certain values of b. It’s why you’ve had to invent exceptions to your made-up bullshit, and pretend 2(8)2 gets different answers when simplified from 2(5+3)2 versus 2(8*1)2.
In other words against the rules of Maths that we have, got it
does not break down, if you have to put add explicit brackets to 1/(ab)
But it does breakdown if you treat ab as axb 🙄
if you have to put add explicit brackets to 1/(ab)
We explicitly don’t have to, because brackets not being needed around a single Term is another explicit rule of Maths, 🙄 being the way everything was written before we started using Brackets in Maths. We wrote things like aa/bb without brackets for many centuries. i.e. they were added on after we had already defined all these other rules centuries before
Mathematics does break down when you insist a(b)2 gets an a2 term
No it doesn’t. If you meant ab², then you would just write ab². If you’ve written a(b)², then you mean (axb)²
for certain values of b
Got nothing to do with the values of b
It’s why you’ve had to invent exceptions to your made-up bullshit
There’s no pretending, It’s there in the textbooks
when simplified from 2(5+3)2 versus 2(8*1)2
You know it’s called The Distributive Property of Multiplication over additon, right? And that there’s no such thing as The Distributive Property of Multiplication over Multiplication, right? You’re just rehashing your old rubbish now
but when multiplications are denoted by juxtaposition, as in 4c ÷ 3ab
Damn, and I thought they were called “products” not “multiplications” 🤔🤔🤔
No it doesn’t. If you meant ab², then you would just write ab². If you’ve written a(b)², then you mean (a×b)²
If you can find an explicit textbook example where writing a(b)² is said to be evaluated as (a×b)² then that’s another way you can prove your good faith (When I say “explicit” I don’t mean it must literally be that formula; the variables a and b could have different names, or could be constants written with numerals, and the exponent could be anything other than 1). Likewise, if you can find any explicit textbook example which specifically mentions an “exception” to the distributive law, that would demonstrate good faith.
I’m not saying that such an explicit example is the only way to demonstrate your claim, but I’m just trying to give you more opportunities to prove that you’re not just a troll and that it’s possible to have a productive discussion. You insist you’re talking about mathematical rules that cannot be violated, so it should be no problem to find an explicit mention of them.
If you think this insistence on demonstrating your good faith is unfair, you should remember that you are saying that the practice of calculators, mathematical tools, programming languages and mathematical software are all wrong and that you are right, and that my interpretation of your own textbooks is wrong. While it’s not impossible for many people to be wrong about something and for me to interpret something wrong, if you show no ability to admit error, or to admit that disagreement from competing authorities casts doubt on your claims, or to evince your controversial claims with explicit examples that are not subject to interpretational contortions, the likelihood is that you’re not willing to ever see truth and there’s no point arguing with such a person.
By the way, sorry for making multiple replies on the same point.
As my own show of good faith, I do see that one of your textbooks (Chrystal) has the convention that a number “carries with it” a + or -, which is suppressed in the case of a term-initial positive number. If you demonstrate it worth continuing the discussion, I’ll explain why I think this is a bad convention and why the formal first-order language of arithmetic doesn’t have this convention.
‘If a+b equals b+a, why is 1/a+b different from 1/b+a?’
ab means a*b.
That’s why 1/ab=1/(a*b).
But we could just as easily say 1/ab = (1/a)*b, because that distinction is only convention.
None of which excuses your horseshit belief that a(b)2 occasionally means (ab)2.
Because they’re not identically equal 🙄 Welcome to you almost getting the point
means, isn’t equal
Nope, it’s because ab==(axb) <== note the brackets duuuhhh!!! 😂
No you can’t! 😂
Nope! An actual rule, as found not only in Maths textbooks (see above), but in all textbooks - Physics, Engineering, Chemistry, etc. - they all obey ab==(axb)
says person still ignoring all these textbooks
Yes we could, because it’s a theoretical different notation. Mathematics itself does not break down, if you have to put add explicit brackets to 1/(ab).
Mathematics does break down when you insist a(b)2 gets an a2 term, for certain values of b. It’s why you’ve had to invent exceptions to your made-up bullshit, and pretend 2(8)2 gets different answers when simplified from 2(5+3)2 versus 2(8*1)2.
No you can’t! 😂
In other words against the rules of Maths that we have, got it
But it does breakdown if you treat ab as axb 🙄
We explicitly don’t have to, because brackets not being needed around a single Term is another explicit rule of Maths, 🙄 being the way everything was written before we started using Brackets in Maths. We wrote things like aa/bb without brackets for many centuries. i.e. they were added on after we had already defined all these other rules centuries before
No it doesn’t. If you meant ab², then you would just write ab². If you’ve written a(b)², then you mean (axb)²
Got nothing to do with the values of b
says person still ignoring all these textbooks
There’s no pretending, It’s there in the textbooks
You know it’s called The Distributive Property of Multiplication over additon, right? And that there’s no such thing as The Distributive Property of Multiplication over Multiplication, right? You’re just rehashing your old rubbish now
Couldn’t resist:
Damn, and I thought they were called “products” not “multiplications” 🤔🤔🤔
If you can find an explicit textbook example where writing a(b)² is said to be evaluated as (a×b)² then that’s another way you can prove your good faith (When I say “explicit” I don’t mean it must literally be that formula; the variables a and b could have different names, or could be constants written with numerals, and the exponent could be anything other than 1). Likewise, if you can find any explicit textbook example which specifically mentions an “exception” to the distributive law, that would demonstrate good faith.
I’m not saying that such an explicit example is the only way to demonstrate your claim, but I’m just trying to give you more opportunities to prove that you’re not just a troll and that it’s possible to have a productive discussion. You insist you’re talking about mathematical rules that cannot be violated, so it should be no problem to find an explicit mention of them.
If you think this insistence on demonstrating your good faith is unfair, you should remember that you are saying that the practice of calculators, mathematical tools, programming languages and mathematical software are all wrong and that you are right, and that my interpretation of your own textbooks is wrong. While it’s not impossible for many people to be wrong about something and for me to interpret something wrong, if you show no ability to admit error, or to admit that disagreement from competing authorities casts doubt on your claims, or to evince your controversial claims with explicit examples that are not subject to interpretational contortions, the likelihood is that you’re not willing to ever see truth and there’s no point arguing with such a person.
By the way, sorry for making multiple replies on the same point.
As my own show of good faith, I do see that one of your textbooks (Chrystal) has the convention that a number “carries with it” a + or -, which is suppressed in the case of a term-initial positive number. If you demonstrate it worth continuing the discussion, I’ll explain why I think this is a bad convention and why the formal first-order language of arithmetic doesn’t have this convention.