Math Is Fun Forum

To : Anthony
Note: very funny way of posting
It could be better if the posts were true.

In Wikipedia, there's a page about unsolved problems:
http://en.wikipedia.org/wiki/Unsolved_p … athematics

Better learn it first.
Linear dependency for vectors basically means, that every has a little "different dimension" form theothers.
Formally, a system {A,B,...,Z} is lineary independent only and only if the equation
aA+bB+cC+...+zZ=0 doesn't have solutions, different from {0,0,...,0} for real a,b,...,z.
For example, if two vectors A,B are collinear, then A=mB, m e R (=/= 0), so
1.A-m.B=0, 1,m =/=0 ==> A and B are dependant.

luca and jane, you're not absolutely right. The notation [.] is an old floor-notation. Today we use \lfloor ect. , but if you look at some notebooks from the 80's, for example, you'll see there floor is [.] . Now [.] is used for another notation.
It's something like the natural number - definition, different in different countries.

you're searching for:

No, no!
Maths is not "invented" by a human.
It's somthing abstract, you can't feel it, touch it, but still "it's there"!
The signs and the equations are just one picture of the math, which the human created.
Mathematics is some kind of invariant. It's unchanged over the universe, it's abstract, and doesn't depend, for example of the length of plank (as in phisycs). It's a mental ocean of knowledges.

But I've ever asked some kind of weird questions : how far can math go? which are the boundaries of the abstraction? Can we do everything with it?
And the other question - what is the structure of mathematics? So far we're proving beautiful theorems in different fields of maths, but no one (with little exeptions) has fully understood a field - that is, to form some kind of intuition to answer some questions whitout proving them.
And another - what is the mathematics made from? And who controls it?
There are weird mathematical paradoxes too, which ;ie in the foundamentals. For example the Goedel's incompleteness theorem - that we can't have math that proves or disproves everything - that maths has limits.
Another interesting contemporary structures are so strange, that nothing can be proven about them at all.
I'll give you an exampe: the infinite random sequence.
Many paradoxes are connected with it. It's proven, that the mantissas of almost every real numbers are such random sequences. But in fact, such sequence is unconstructible! There's no example of truly random infinite sequence!
Another example, which is more fascinating, is the halting probability : the probability arbitary computer program to halt.
It is shown that this probability exist, and is between 0 and 1, but is algoritmically unpreictible - that is, we'll can never know what is, for example, its 100th digit!

Is the mathematics inconsistent? Nobody (with little exeptions) knows. And we can't be sure until we find a crack in it.
But after 30000 years evolution, we've still not understood the "mattery" of the mathematics - the language of the universe we live in.

Again the old story!
Anthony, just try to beleive all the people telling you that
0.999... = 1!

I told you - the question is wrong. There doesn't exist any x satisfiyng the conditions.

Excellent! Good obsrvation, toast!
The answer is simple: just:
477...773 = 11..11*43 (k 7's and k+1 ones)
377...774 = 11..11*34 (k 7's and k+1 ones)

But it's interesting.

Here are two plots, made them with mathematica.
The first is for all numbers to the 100000th prime number (not 100000)!
The second - to 1000000th prime number:

Intersting.
There's a conjecture, that for every even n, there exists infinitely many prime couples (p,q), such that p-q=n.
Intersting pattern.
Does your avatar has some connection with this?
I like it very much.

You can upload images, using "upload image", when you're posting and using  the

[img]

tag.
Something like:

[url]http://the_place_where_your_image_is[/url]

You can also read the forum features.

Some plots: