Because they don't contradict any of your other definitions, and none of the things you can prove with those definitions contradict one another either.
This is what maths is all about - trying to find a set of principles from which we can prove useful stuff, without making contradictions.
When you test it out of the fishbowl, get back to us, let us know how it turns out, now, will you?
Now, oddly enough, you can prove that you can never get a system of principles in which you can prove or disprove everything but which is consistent. You can, however, get closer and closer to such a system
(This is called Gödel's incompleteness theorem)
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!
Concepts don't change; they're abstract.
What will change is where the PO abstract meets the non PO road!
It's irrelevant to the truth of mathematics, yes.
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??
I told you before that if a function "goes to infinity" at a point (which we will call a) then:...
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!
For any positive M, there exists a d such that, for any x around some region near a, whenever the distance from x to a is less than d, the distance from f(x) to f(a) is greater than M.
Positive M? In some
region?? Would that happen, by the by, to be in the fishbowl??? Better try a little harder than that. My, baby math can be cute, and funny.
This last part we write as:
(|x-a| < d) --> (|f(x)-f(a)| > M)
Well, a lot of IFS go into the stuff that you feel turns our greater than M. That much seems evident.
OK, so first I'm going to prove that the function f(x) = 1/x fits this definition.
We can pick any M we like as long as it's greater than zero.
OK, let's pick the 5 loaves there. Something to get our teeth into.
So suppose we've picked it, and now we're going to keep it fixed, whatever it is, for the rest of the proof.
That's what you think!
We've not actually said what we've fixed it as, but it can't vary from one step to another.
I think we are getting to the root of baby math's problem here. They can't fix squat out of the fishbowl!!!
Now we need to find some d such that the above is true. So we'll say that d is the least of 1 and 1/M - both of these are positive, so that's fine.
Well, no, because by now, people started eating, and we have more loaves already. It only gets worse for your fixing attempt from here.
Now, we assume that |x-a| < d - because if it isn't it doesn't matter; we only need to prove stuff for when this is true.
Well, no, assuming is dangerous, if it depends on how you fix things in the present state universe fishbowl.
Now, if this is the case, then it is also the case that x - a < d. And d, we said, was 1/M or 1, whichever is least, so we know that d is less then or equal to 1/M.
hence x - a < 1/M.
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.
Now, for 1/x, we are trying to prove that this goes to infinity at 0 - so a=0 - so we get:
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.
Multiplying by M then dividing by x we get:
M < 1/x or equivalently 1/x > M
Which was exactly what we wanted - i.e. to show that, if |x|<d, (because a is 0) then 1/x - 1/0 was larger than M (whatever we picked M to be)
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.
So 1/x fits the definition. Now, we want to add 1 to infinity. So it would be reasonable to ask what is "1/x + 1" as x tends to 0. I claim it is infinity as well. Now to prove it.
There we go again with claims of infinity, and beyond. Give it up. Your numbers don't really cover that. Stick to the real world.
Just as we did before, we're going to say, pick an M, any M, as long as its greater than 0. Now, hold that fixed and I want to prove that:
(|x| < d) --> (|1/x+1|>M)
So this time I'm going to take d to be the least of 1 and 1/(M-1) (note that if M is less than 1, then this would make d negative, we can ignore this though, because we can verify by hand that 1/x goes greater than 1)
Then, as with last time, if |x| < d then certainly x < d. And we know that d is less than or equal to 1/(M-1) so:
x < 1/(M-1)
M-1 < 1/x
1/x + 1 > M
Which was what we wanted.
But you never got it, because M was 5 loaves, and it never obeyed your fixing attempts. Soon, the whole forever universe will do likewise. See how small baby maths are?? Thanks for that demo.
So I have not only told you that infinity + 1 is infinity, I have proved it beyond question.
So... What was your point?
Point is that you have only fixed your imagination, and forgot to fix that to reality of either the spiritual added present, or the forever state future.
Yeah, the mathematicians say you're welcome for the encryption that ensures people don't steal you credit card details.
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.
And for the maths behind the physics that probably helps power your home, and the logic which got the computer you're using working!
Good thing there are mathematicians who are willing to waste their own time so you don't have to!
Hey, it takes all kinds. Long as they use their numbers for good, and not evil, I think that we all can relax.
I don't know how you would know! But that one would still be 20%!
That is the point, when projecting present math onto a reality that has more than the fundamental underlying concepts of baby math were designed for. But, I suppose that particular equation would depend on the way the loaves were replicated. For example, if the 5 loaves at one point added up to 11,111 loaves, 20% would be 555,55 loaves. No?? Yet, if the loaves were all whole, how does that work??
Well duh, that's because 1 out of 40,000 isn't the same percentage as 1 out of 5. This is news?
No, I think it would be more like the point.
No. 20% of 5 is 1. 20% of 5 blims is 1 blim even if no blim exists, has existed, or ever will exist.
Your percentages don't seem to reflect the loaves, as a whole blim.
What mathematical function is supposed to be continuous or not, here?
"The
mathematical concept of a
function expresses dependence between two quantities, one of which is given (the
independent variable, argument of the function, or its "input") and the other produced (the dependent variable, value of the function, or "output")." wiki
So, the dependence between the 5 loaves, and the rest is not something that is a function of baby math.
Only if you think death is doom.
I do. How much worse could it get??
I mean, some of these poor jokers now even suggest we hasten the demise of the entire universe, just by looking at it!!! Talk about the depths of madness!
"
A shocking new theory in the world of physics suggests that we might have accidentally brought the universe closer to its death, just by looking at it. The observation of the dark matter back in 1998, which is thought to be responsible for the acceleration of the cosmic expansion, may have caused the universe to shift to a state similar to one in its past, in which the universe had more chances to end.
"
http://news.softpedia.com/news/Don-039-t-Look-There-The-Universe-Will-End-71572.shtml
Behold, the theory!
Huh? Nobody knows whether our universe will be destroyed.
How about scientists, in a Time magazine article?
"
THE FATE OF THE COSMOS
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"
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!!!??
