When you test it out of the fishbowl, get back to us, let us know how it turns out, now, will you?
A contradiction doesn't change depending on the universe. 1=0 is a contradiction whichever way you slice it.
Well, my hat's off the the smart fellow that had enough sense to at least realize man's knowledge is incomplete. I would elevate that concept all the way up to a demonstrated fact!
It's a proven fact, and it's a proof which you couldn't even begin to comprehend.
What will change is where the PO abstract meets the non PO road!
There
is no "PO" abstract. The abstract has nothing to do with physics whatsoever.
The truth of mathematics?? Is that like where we add stuff to an unknown, imaginary infinity as a numberless number, and limit the amount of loaves available to feed people??
No.
Then, how would you prove that it actually did any such thing? You wouldn't even know what it was if it ever got there!
I'm about to prove that it does such a thing, but it will never
get there. If it
got there then
there wouldn't be infinity.
Positive M? In some region?? Would that happen, by the by, to be in the fishbowl???
No. That would mean anywhere on the real number line within a given distance of the point we're testing. For normal, everyday functions like 1/x the region is actually the entire domain of the function, but for less "nice" functions you might need to restrict that.
Well, a lot of IFS go into the stuff that you feel turns our greater than M. That much seems evident.
"IFS?"
OK, let's pick the 5 loaves there. Something to get our teeth into.
"5 loaves" is not a number. We can pick five, if you want.
No, that's just how it works.
I think we are getting to the root of baby math's problem here. They can't fix squat out of the fishbowl!!!
You can't have M vary from one part of the proof to another. That would be stupid. All it matters is that, at the start, you can pick any M, so long as you keep it the same until the end. Then if you like you can pick any other M and start again.
Well, no, because by now, people started eating, and we have more loaves already. It only gets worse for your fixing attempt from here.
So, is M 5 or isn't it? Pick a number for M and I can show you how it actually works.
Well, no, assuming is dangerous
Since I just told you why it isn't dangerous, I will ignore you.
You no longer even make any sense, because things were anything but fixed. Man needs to know they are broken, before we look to God to really fix us. That is Higher math.
You mean you don't understand a little bit of first-year analysis? Aww. Poor you.
Oh, no, not that silly Buzz Lightyear stuff again. Face it, you can't go to infinity and beyond, and you can't even send your numbers. Such is the real world.
As if you had the slightest clue what either now represented.
x is the number we put into the function. We're going to vary x around 0 to see what happens.
< means less than
M is any positive number you please
1/M means the reciprocal of M. If you have a sausage of length one, and you divide it into 5 equal pieces, then the length of each piece is the reciprocal of five.
Hey, you are pretty good at math, we can say that much. But, since the M was fixed as out of the present nature rules, your numbers fall by the wayside as meaningless.
No, this is just elementary analysis - It's just more advanced than you're used to. But M was just fixed to whatever number you started out with. Changed your mind? Start again, but you can't change your mind half-way through.
But you never got it, because M was 5 loaves
M is a number. Is a loaf a number? No - it's a piece of bread. How can multiply a loaf? What happens if you take the square root of a loaf? Is a carrot less then, more than or equal to a loaf? Stick to numbers, you'll have less trouble.
I'll show you how it works. Suppose you pick M as a number (in a fit of sanity) and you give me 5 as a first guess. Now I say, according to my rule, that
d is equal to the lesser of 1 and 1/(M-1). Well 1/4 is less than 1, so that's d.
d represents the distance x is going to be from 0. so |x| < d which is just the same as saying |x| < 1/4.
Well, if the distance is < 1/4 then x on its own is certainly < 1/4.
So 4 < 1/x.
So 5 < 1/x + 1.
So the rule works - if we pick
d equal to 1/(M-1) then we will always end up with 1/x + 1 more than M - whatever you care to pick for it. If you give me 1000, the same works, you end up with this:
x < 1/999
999 < 1/x
1000 < 1/x + 1
See? Simple.
So, what does all this mean? It means that, no matter
how large a number you pick, I can always give you another number, dependent on the one
you picked, such that whenever x is closer to 0 than my number is, 1/x + 1 is bigger than your number.
That, in turn, means that 1/x + 1 gets
bigger than any number you give me (as x goes to 0). And that means 1/x + 1
tends to infinity.
Point is that you have only fixed your imagination
It's fixed in the proof, and that's what matters.
They failed. But it was a nice try. They might have to stick the numbers in people's head to get real secure. But I give them A for effort, in a real world endeavor there.
Someone broke the encryption? They don't need to steal credit card details - they can get $1,000,000 off the Clay Mathematics institute, for starters, more than likely!
Actually what happened was that someone took your data when it wasn't encrypted.
No, I think it would be more like the point.
Your point is pretty boring then, I'm afraid.
So, the dependence between the 5 loaves, and the rest is not something that is a function of baby math.
You were talking about the sun or something. Is there a continuous function there?
I do. How much worse could it get??
Being in pain?
http://news.softpedia.com/news/Don-039-t-Look-There-The-Universe-Will-End-71572.shtml
That means that the 100 billion or so galaxies we can now see though our telescopes will zip out of range, one by one. Tens of billions of years from now, the Milky Way will be the only galaxy we're directly aware of (other nearby galaxies, including the Large Magellanic Cloud and the Andromeda galaxy, will have drifted into, and merged with, the Milky Way).
By then the sun will have shrunk to a white dwarf, giving little light and even less heat to whatever is left of Earth, and entered a long, lingering death that could last 100 trillion yearsor a thousand times longer than the cosmos has existed to date. The same will happen to most other stars, although a few will end their lives as blazing supernovas. Finally, though, all that will be left in the cosmos will be black holes, the burnt-out cinders of stars and the dead husks of planets. The universe will be cold and black.
But that's not the end, according to University of Michigan astrophysicist Fred Adams. An expert on the fate of the cosmos and co-author with Greg Laughlin of The Five Ages of the Universe (Touchstone Books; 2000), Adams predicts that all this dead matter will eventually collapse into black holes. By the time the universe is 1 trillion trillion trillion trillion trillion trillion years old, the black holes themselves will disintegrate into stray particles, which will bind loosely to form individual "atoms" larger than the size of today's universe. Eventually, even these will decay, leaving a featureless, infinitely large void. And that will be that"
Well, if that's true, then the universe will just be boring, not destroyed. Somewhat different. It will also be billions of years in the future, when we won't actually be alive to care.
http://www.time.com/time/covers/1101010625/story.html
How DARE you accuse those that preach everlasting peace, life, and love, by Jesus, as gloom and doomers!!!??
You never read Revelation then?