/sci/ - Science & Math

[Anonymous No.5168040]

If we have an equation:
<span class="math">
x = y
[/spoiler]
where x and y are some mathematical expressions, and we want to show it's true so we reduce it down to
<span class="math">
1 = 1
[/spoiler]
by manipulating both sides or only one side.

what kind of proof would this be classified as or is it even valid?

[Anonymous No.5168044]

You can only do that if you use iff in each logical step otherwise the premise won't be implied by the conclusion.

[Anonymous No.5168048]

Set x=-1 and y=1
x = y
-1 = 1
(-1)^2 = 1^2
1 = 1

[Anonymous No.5168051]

>>5168044
Okay, so as long as I don't do something like:
<span class="math">
1 = -1
[/spoiler]
hurr, square both sides
<span class="math">
1^{2} = {-1}^2
[/spoiler]
<span class="math">
1 = 1
[/spoiler]
?

[Anonymous No.5168056]

>>5168051
Start with one side and then do shit until it looks like the other side. Dont touch the other side.

[Anonymous No.5168059]

>>5168048
>>5168051

[Anonymous No.5168071]

If you want to proof x = y. Just show that

x - y = ... = 0
This does indeed imply x = y. It is mathematical correct and less work than what you are trying.

[Anonymous No.5168119]

So would the following not be valid?

<span class="math">
1+\sum_{i=1}^{n}{2^{i-1}} = 2^{n}
[/spoiler]
<span class="math">
2^0+2^1+2^2+\dots +2^n = 2^{n}-1
[/spoiler]
<span class="math">
1+2(1+2(\dots )) = 2^{n}-1
[/spoiler]
<span class="math">
2(1+2(\dots )) = 2^{n}-2
[/spoiler]
<span class="math">
1+2(\dots )) = \frac{2^{n}-2}{2}
[/spoiler]
<span class="math">
1+2(\dots )) = 2^{n-1}-1
[/spoiler]
<span class="math">
\dots
[/spoiler]
<span class="math">
1+2(1) = 2^{n-n-2}-1
[/spoiler]
<span class="math">
2 = 2^{2}-2
[/spoiler]
<span class="math">
1 = \frac{2^2-2}{2}
[/spoiler]
<span class="math">
1 = 2^1-1
[/spoiler]
<span class="math">
1 = 2-1
[/spoiler]
<span class="math">
1 = 1
[/spoiler]

[Anonymous No.5168133]

>>5168119
No!
Just do a fucking induction.

[Anonymous No.5168134]

>>5168133
okay

[Anonymous No.5168190]

>>5168119
All the "..." stuff is frowned upon at best, but the general form of the proof is fine.