Post by Eugene 2.0 on Jul 29, 2021 20:48:58 GMT
It's so hard to believer I never know this rule before. I should discover it earlier, but I don't know why it never happened. Anyway, if someone doesn't know or maybe forgot this, I'd like you to recall it from your memory or to note it there, and maybe it'll help you.
x1, x2, ..., xn; y1, y2, ..., yn- are any algebraic members or monomial (or polynomial) members;
A base rule: (x1 = y1) & (x2 = y2) → (x1 + x2 = y1 + y2)
x1 = y1
x2 = y2
----------
x1 + x2 = y1 + y2
And an extended version: ∀x,y(xi=yi) → Σ(xi=yi)
x1 + x2 + x3 + ... + xn = y1 + y2 + y3 + ... + yn
An example:
1+2+3 = 6
4+5 = 32
-------------
1+2+3+4+5 = 32+6
The backward formula (x1 + x2 = y1 + y2) → (x1 = y1) & (x2 = y2) logically isn't tautology (or it's just consistent), but this one rule is the main algebra rule. So, this law above demonstrates what algebra does. Let's correct it a little to show this:
(a + b = c + x) → (b = c) & (a = x)
Then, finding all formulas like (b=c), we're eliminating just completed arguments to get the main argument that has x. In our formula it's (a=x). So, as soon as we get it, we're close to the answer. And we have to say that our answer - is that last conjunction.
x1, x2, ..., xn; y1, y2, ..., yn- are any algebraic members or monomial (or polynomial) members;
A base rule: (x1 = y1) & (x2 = y2) → (x1 + x2 = y1 + y2)
x1 = y1
x2 = y2
----------
x1 + x2 = y1 + y2
And an extended version: ∀x,y(xi=yi) → Σ(xi=yi)
x1 + x2 + x3 + ... + xn = y1 + y2 + y3 + ... + yn
An example:
1+2+3 = 6
4+5 = 32
-------------
1+2+3+4+5 = 32+6
The backward formula (x1 + x2 = y1 + y2) → (x1 = y1) & (x2 = y2) logically isn't tautology (or it's just consistent), but this one rule is the main algebra rule. So, this law above demonstrates what algebra does. Let's correct it a little to show this:
(a + b = c + x) → (b = c) & (a = x)
Then, finding all formulas like (b=c), we're eliminating just completed arguments to get the main argument that has x. In our formula it's (a=x). So, as soon as we get it, we're close to the answer. And we have to say that our answer - is that last conjunction.