Are math proofs ever valid?

[ShawnD1]

I was reading a joke site with a bunch of math proofs and it got me thinking. Why the heck do we proove stuff in school if we can easily show that math prooves absolutely nothing? Look at these

Theorem : All numbers are equal to zero.
Proof: Suppose that a=b. Then
a = b
a^2 = ab
a^2 - b^2 = ab - b^2
(a + b)(a - b) = b(a - b)
a + b = b
a = 0

From: Chris Trevino
And Furthermore if a + b = b, and a = b, then b + b = b, and 2b = b,
which mean that
2 = 1


Another one

Theorem : 3=4
Proof:
Suppose:
a + b = c

This can also be written as:

4a - 3a + 4b - 3b = 4c - 3c

After reorganising:

4a + 4b - 4c = 3a + 3b - 3c

Take the constants out of the brackets:

4 * (a+b-c) = 3 * (a+b-c)

Remove the same term left and right:

4 = 3






Theorem: 1$ = 1c.
Proof:
And another that gives you a sense of money disappearing...

1$ = 100c
= (10c)^2
= (0.1$)^2
= 0.01$
= 1c




If we can make anything equal anything by using technically correct math, what is the point of trying to prove a theory using math?

[frankjcrow]

Why use math? Its really nothing more than another language of sorts. What would nerdy engineer/mathematician types do with themselves otherwise?

I like your "proofs", but you know, they are not 100% correct per se, right?

Besides using 100% correct proofs you can do things that convince people that they don't like math:

When is "1 + 1" not equal to 2? When it's in binary!

Likewise, what's wrong with this simple addition problem:

7135
+ 643
----------
10,000

you're right! absolutely nothing! (it's in octal)


And why learn anything more than addition anyway? That's the only arithmetic function that microprocessors can perform.

Yes, your high and mighty P-4's running at a bazilla-hertz only know how to add! (and shift, but that's not an arithmetic function)

Subtraction is calculated by adding the two's complement of the subtrahend. Multiplication is performmed along the lines of repetitive addition (actually, shifting helps here) and of course division is repetitive subtraction.

Nevermind the fact that these processors spend most of their time doing nothing! And when they do "nothing" (a nop - no operation) they do it faster than almost anything else on earth...nothing but nothing can do nothing faster than a computer! (which is what they are doing most of the time)

Some people tell me that they don't know what their computer "does" from time to time. I do! It's simple, it's either adding, shifting or doing nothing...really fast...I'd bet money on it!

Since doing "nothing" is sorta related to zero, lets take a look at the problem(s) inherent in those "proofs":

Anything times zero is zero right?

So:
for all "x"

x * 0 = 0

and for any "y"

x * 0 = y * 0

Both sides equal zero so the equation remains true right?

Would it be then legal to divide both sides by zero (!) to
get:

x = y

?

Of course not!

But bottom line, math is neither here nor there, the best thing about it, in my opinion is that it affords one an excuse to discuss nothing with sometimes very interesting people. ;D

-Frank Crow

[jkrohn]

Your question should really be "Why use Math correctly?"

If I incorrrectly use anything then of course it will look false. Your "proof" contains a well known logical fallacy. If you are insterested in your errors, see here
http://mathforum.org/library/drmath/view/57116.html

For a more genel overwiew of this and other common "proofs" see here.
http://mathforum.org/dr.math/faq/faq.false.proof.html

Jkrohn

[muno]

Interesting, and I actually understood it, which makes it even more interesting
-M

[Theophylact]

Lewis Carroll has an amusing argument that the very structure of logic requires that any proof requires an infinite number of assumptions.

[ShawnD1]

What about the question where you multiply by 4-3? Technically it's multiplying by 1 which is perfectly legal. Any ideas?

[jkrohn]

Theorem : 3=4
Proof:
Suppose:
a + b = c

This can also be written as:
4a - 3a + 4b - 3b = 4c - 3c
After reorganising:
4a + 4b - 4c = 3a + 3b - 3c
Take the constants out of the brackets:
4 * (a+b-c) = 3 * (a+b-c)
Remove the same term left and right:
4 = 3

Multiplying be one? Lets examine TWO steps her
a+b=c
and
4 * (a+b-c) = 3 * (a+b-c)

As per your initial statement, a+b=c so a+b-c = ZERO

Guess what, 4(0) = 3(0) or to generalize it more a(0) = b(0) for any a,b belonging to the reals.

What is wrong with your proof? Simple, you cannot divide by zero, which a+b-c is per your initial assumption.

Jkrohn

[Pexster]

If a + b = c, then

a + b - c = 0

which makes the last division invalid, because we know that
division by 0 is undefined.

(Sorry, I was a split second too late!)

[jkrohn]

And not to debunk your last time.
Theorem: 1$ = 1c.
Proof:
And another that gives you a sense of money disappearing...
1$ = 100c This is a declaration. $ and c may as well be a and b. a = 100, b = 1. These are quantifiers and are necessary to make your equation work.

= (10c)^2 This cannot work since c is a quantifer. You get 100c^2. Though since c = 1 and 1^2 = 1 your mistake deson't crucify you as it should.
= (0.1$)^2 = 0.01$^2 Since $ is a quantifier and not one, this crucifies you this time., this is .01 * $ * $

You can evaluate as many of those as you like, but I will choose to evaluate one. 0.01 * 100 * $ = 1$

Any other "proofs" you need "proven"?

Jkrohn

[wallie_x]

Shawn1D sez:
"Are math proofs ever valid?"

If we interject evolutionary thought into the above idea we postulate then that, due to existential dread, we sentient 'super monkeys' must somehow validate our perceptions as real or it makes us all unequivocally full of crap. So we use abstractions as if they were absolute ends in themselves to justify our uniquely human machinations about the universe.
Even if our musings are empty of real content, at least we have fooled ourselves into believing the converse. It is the only way we can be at peace with ourselves, and at the same time believe that our lives ultimately have at least some sort of meaning.