Math proof

[ELorenz]

If anyone has any problems they would like to present to see if someone can prove them that would be a good exercise to. I'll put this one out there.( as a general statement, don't put your homework problems up here though ).

See if you can come up with a proof for DeMorgan's law, (A union B)^c = A^c intersection B^c. I'm using ^c to denote compliment.

Here's another proof to go through also. There are a whole lot of things wrong with this proof see if you can find them all.

Show that a + t^2 is a subspace of the polynomials given that a is a scalar and t is a variable.

take two vectors of the form a + t^2 and show that vector addition holds. Let a and b be arbitrary scalars, (a + t^2) + ( b + t^2 )= (a+b) + 2(t^2)= divide through by 2 = (a+b)/2 + t^2, so it's of the form a scalar added to a variable, so it's closed under addition.

Now show that it's closed under scalar multiplication. Let c be an arbitrary scalar, then c(a+t^2) = ca + ct^2 = ca/c + t^2 which is of the right form, so it's a subspace.

The correction to the composition of functions proof was correct

[TheMindRapist]

What do you guys make of this?

_
.9=x
_
10x=9.9
_ _
10x - x = 9.9 - .9

9x = 9

x = 1
_
.9 = 1

Can you spot the mistake?
Or is there one?

[ELorenz]

The problem is that you are not being consistent with what you're doing with the equation. If you subtract x from the left side you have to subtract x from the right side. so the equation would have to look like 10x - x = 9.9 - x, or 10x - .9 = 9 - .9. Even though x = .9 you can't interchange the two when manipulating the equation, you have to use the same thing for each side for an operation. That line is what leads to the incorrect solution.

It was a nice idea unfortunately incorrect

[comperr]

Heh - I used to make these up daily in boring math professors classes.

Here is a recent one: I used wikipedia code for it cause its hard to type out

Code: Select all

<math>\sum_{n=5}^\infty \frac{n}{1} = \infty</math><br />
<math>\sum_{n=6}^\infty \frac{n}{1} = \infty</math><br />
<math>5 + \sum_{n=6}^\infty \frac{n}{1} = \sum_{n=5}^\infty \frac{n}{1}</math><br />
<math>5 + \sum_{n=6}^\infty \frac{n}{1} - \infty = \sum_{n=5}^\infty \frac{n}{1} - \infty</math><br />
<math>5 = 0</math><br />


[comperr]

Oh and no one add it to the page - I want to add it myself tommrow

[TheMindRapist]

Heh, the _'s didn't space properly, I meant .9 to be .9 repeating infinitely, as in
.9999999999999999999999999999999999999999999999999999999999
ect

[comperr]

http://en.wikipedia.org/wiki/.999

[ELorenz]

Interesting, I haven't ever run into that before, but I don't know that much about real analysis or series.

Was the last one I posted too much?

[krauser2288]

*EDIT*
just forget it........

[Jimmy_xor]

krauser2288, please remove that or I will report you...