## Wednesday, September 21, 2016

### Charlotte Fatalies

Charlotte protest: fatal 'civilian on civilian' shooting as violence erupts – live | US news | The Guardian

Man fatally shot in Charlotte protests over US police shooting - BBC News

Man fatally shot during Charlotte protest against police shooting, city says - The Washington Post

New Protests Erupt in Charlotte as Accounts of Police Shooting Diverge - The New York Times

Man fatally shot in Charlotte protests over US police shooting - BBC News

Man fatally shot during Charlotte protest against police shooting, city says - The Washington Post

New Protests Erupt in Charlotte as Accounts of Police Shooting Diverge - The New York Times

### Julia - GÃ¶del 4

4

It
might seem that there is no connection between finding longitude, and
finding a way to have just one connection, as opposed two. It might
seem that these are separate problems requiring separate solutions.
And for the 18

^{th}century this was the case, but then Georg Cantor drifted in. There were two pieces that he contributed. First, he found that infinity is different from finite, and then issued that there were at least two kinds of infinity: the natural number, and the, though we don't see this way in pure mathematics, real number. In this chapter we will deal with what this means, and why it is important.
There
are some mathematicians who do work, and they do not attract any
attention. Such as Leonard Euler, who made many contributions and, as
far as the historical eye can see, did not raise any failures. This
despite making important discoveries in different fields such as a
infinitesimal calculus, among a host of others. Then there are
mathematicians who generate controversy, this is the fate of Georg
Cantor. Who became known for the important one-to-one correspondence
between numbers. He came to mathematics not describing any infinite
set theories, and left it by proving there are an unlimited number if
infinite sets, and there are at least two separate infinite sets
which are not countable between each other. What he did not prove, is
if there are only two.

Now,
numbers had been known to be irrational, that is not countable for a
very long time, but what this did not take into account was there
were numbers that were countable, and numbers which were not
countable, and that both of these sets were infinite, and infinite in
two separate ways. In other words, there was unlimited but countable,
and unlimited and not countable, and these were different sets of
numbers. Moreover, a small number of the countable numbers was
exactly the same as a much larger share of them, and both of these
were

*the same number.*
Think
about squares. It is obvious that there are more numbers that are not
square then squares. It is also obvious there are the same number of
squares, as numbers that are not square. It seems to be a
contradiction, how can there be more not squares than squares, and at
the same time an equal number of squares and not squares?

This
is where Cantor fits in. Is more famous method is coming on the
diagonals. What he does is show that numbers, such as 1, 2, 3, 4 and
so on are the same as 1/2, 2/3, 3/4 and so on, that there is a 1 to 1
correspondence between two sets. There is a one-to-one correspondence
between a finite number, but there is between an infinite number.
First he shows that this could not be the case because there are an
infinite number of 1/2, 2/3 and so for each 1, and so on. But he then
counts not up-and-down, nor across, but along the

^{diagonal}. Then Cantor showed that there was an uncountable set, which had more members than number of countable but unlimited sets. These were sets which didn't end. Remember while there were unlimited number of numbers, the countable sets individually had a name – 1/2 for example, even if they did not have a name but could theoretically have a name, that made no difference. But numbers which could not be count, even by an infinitely patient man, were different. These are things such as pi, which my computer does not let me represent, our different. Thus there are two sets of infinite numbers, Countable and uncountable.
Realize
immature amateur mathematicians still come up with a proof that they
can “square the circle”, that is with a straight edge and compass
built a square which is the same as a circle. And perhaps always will
do so. I suppose it's one of the tests for an amateur mathematician.

What
he does is divide the proof into two parts. The first part takes a
random sequence of real numbers, x

_{0},x_{1},..x_{n}and a set of coefficients pairs [a,b] which has at least one pair is not part of the real numbers. He does by selecting pair of coefficients where a is increasing, and b is decreasing; and every member of a is smaller than every member of b. Then he breaks in to two cases: as said the finite case and the infinite case. If it is the finite case, then only one number can be inside a_{n},b_{n}. If it is of the infinite case then he doesn't need to counter, because, x_{0},x_{1},..x_{n }is not in infinite order, remember that they are finite by definition. Actually, he goes one step further, one case where a=b, and the other one where a < b.
Let
me take and example: 6x

^{2}+9x+5 it would become (1)(5)x^{0}+(2)(3)x^{1}+(3)(3)x^{2}.
What
Cantor does is the orders of the coefficient by their heigh and then
orders, then orders the real roots by the same height, and shows this
cannot be counted, either by infinite or finite means. This is not
the normal way of doing things, but it is Cantor's way of doing
things. And this is basically the first proof he ever publishes.

Cantor
discussed the proof with Dedekind, and pointed out that it would be
of interest if this proof could have produced a new theory of
Liouville's that numbers are valid. He tries to do this in a proof,
but it needs an additional proof, which he then supplies. He then
announces just for Christmas 1873 a proof which not only answers
whether the real numbers are counted, but that there are
transcendental numbers. But Cantor realized that this was a bridge
too far. So he omits this, and returns to prove with the first, that
is the second proof, which he publishes.

That
could be the end of Cantor's story.

But
isn't yet, having proved there one time of countable infinity, he
next proves that there is an uncountable kind of infinity, which is
larger than the countable kind, but he doesn't know if the number of
the continuum, which is what he calls it, is the next number in the
sequence of uncountable figures. Thus he makes the first prove of
zero, but he does not make the second proof of one, because he
doesn't know if there is something beneath his second proof that his
larger then the proof of zero, which he knows his the smallest kind
of infinity, but he doesn't know if there is a larger infinity then
the countable numbers, but smaller than his proof that uncountable
numbers. In other words, he doesn't actually know, though he and we
are pretty certain that it's true, that all of the numbers such as pi
are really the next set of numbers. And this has been true for almost
a century, we don't know that pi, and the other countless unending
numbers are the next in the sequence. But as I said, most people are
pretty sure. It's just that “pretty sure” it is not the same as
“proven to be”.

And
no one who is in their right mind is sure that “proven to be”
really is true. Note that cantors proof doesn't mean that the numbers
of x need to be countable numbers, they can be uncountable numbers,
but each one needs to be a specific number, even though you don't
know which member it is. This is strange that you may not know
exactly which number it is, but you can say that it is a specific
number.

So
Cantor is known for the following ideas:

- There are a countable number of numbers.
- There are an uncountable number of numbers.
- The number of uncountable numbers is larger.
- There may be, though it is unlikely, that there may be a set between the first two which is larger than the countable numbers, but smaller than uncountable numbers. But, as quantum physics says, if it is not absolutely, then somewhere it is.

And that will leave a mark that
people will remember for at least 100 years. So he not only proved
that to things that seemed different, are not – by counting on the
diagonal. But he also showed that two things that are the same,
actually are different by counting within the sets. Irrational
numbers are different from rational numbers.

What Cantor did not prove, though
he tried, was that there was an uncountable number of uncountable
things. That is to say, the number of the continuum is both the next
number in his aleph series of numbers, and not the next. It is
uncountable, and that means that there is not just one infinity,
which we live in – but an infinity of infinities, which branch off
in two ways – the number of uncountable infinities is both the next
number, and not the next number. And even deciding which to do leaves
the other one in place.

In other
words, Canter was a great man, but left more room for an even greater
man, whose name is not yet recognized.

### Hillary Clinton: My Plan for Helping America’s Poor

Hillary Clinton: My Plan for Helping America’s Poor - The New York Times

This is the wrong way to do it.

This is the wrong way to do it.

### For Clinton, attacking Trump may not be enough

For Clinton, attacking Trump may not be enough - The Washington Post

The Baby Boom is no longer the only game in town, and there are no where near enough millennial's who are rich. You need to promise them something, not just say that you will let the Republicans take everything they have.

The Baby Boom is no longer the only game in town, and there are no where near enough millennial's who are rich. You need to promise them something, not just say that you will let the Republicans take everything they have.

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