Post by Alan MackenziePost by Mitch RaemschPost by Alan MackenziePost by Mitch RaemschPost by Alan MackenziePost by Mitch RaemschPost by Alan MackenziePost by Mitch Raemschif you draw a number line it has a zero boundary beginning
followed by a first positive... or sub finite real as the
unlimited small.
If you draw the real number line (that's "real numbers", not "real
(i) It extends indefinitely in both directions;
(ii) Zero is on the line;
(iii) There is no smallest strictly positive number on it;
What about the first negative quantity?
There is no such first negative quantity, either.
So what comes first after zero when you draw
a number line?
You're obsessed with this idea that something must "come first".
What is next to zero? You are obsessed with trying to get rid of it...
Not at all. How can one get rid of something which doesn't exist?
The fact is, mathematicians over the last few centuries have sorted out
all these things about "infinity" infinitesimals, "being next to", and
so on. That stuff is all solid knowledge now, and you insisting on
there being something on the real line "next to zero" is about as clever
as asserting that the Earth is flat.
Mathematics is a matter of rigorous proof, not a matter of opinion.
Several people here, including me, have given you a proof that your
supposed "first number next to zero" can not exist. Yet you ignore this
proof. Maybe you haven't made the effort to understand it. I recommend
you to go back and do that now. If you really can't understand it, then
I would recommend you simply to accept it on the grounds lots of other
people over the centuries have checked it and found it to be true.
Okay, here's the thing in simplistic terms. Anyone older than three
and with an I.Q. larger than their shoe size pleas bear with me to
the end. I *know* I'm not being rigorous but rigour doesn't do the
trick with Archies and Mitches. Maybe comedy will?
So, let us begin:
We have Zero, a number. We *display* this number as a point on a line
that we call "The Real Number Line". This is only a drawing, a model,
a *picture*, not reality but let us work with it.
To the "right" of Zero we have lots and lots and lots of positive
numbers and to the left just as many [hmmm, is that true?] *negative*
numbers.
Archaic Poo and Mr Gabriel are wrong. Negative numbers do exist and
they can be *pictured* using our little line. [Well, they do exist
just as existy as positive ones do and there is *probably* just as
many of them. Maybe. Well, it's got a fair chance of being so.]
Now, look at Mr. Zero, sitting there in the "middle", all fluffy and
round and cosy. Nice, yes? Okay, so we are going to walk from Zero
along our line to some very, very small number that is nearly Zero. So
we start our journey at "the very smallest number right next to Zero"
[let us call this number "Hunny" because Hunny is very close to me
and, in Mathematics, I'm about as close to a person of zero skills as
can be] then jump to the next most close number "Hunny plus a littly
bit", then the next and the next and so on until we get to the number
we first thought of.
So far, so easy, yes?
So, exactly how small *is* Hunny? *How* "close to Zero" is she?
Well, she's bigger than half-a-Hunny, isn't she? That seems obvious
as half a cake is smaller than the whole cake was. She's even bigger
than a Hunny divided by four and Hunny-over-twenty and a ten thousand
millionth of a Hunny.
Let's see, we can call "a ten thousand millionth of a Hunny" "Bob".
So, Bob must be smaller than Hunny, yes? After all, Bob is Hunny
*DIVIDED BY* 10,000,000,000 so it must be smaller. Sort of like the
way a single Mitch is smaller than the entire population of Man.
But ... if Bob is *smaller* than Hunny, that means Bob is CLOSER TO
ZERO than Hunny.
Oh. Oh, dear. Oh, deary, deary me. That means that my lovely little
Hunny is *not* now the closest number to Zero, Bob is lots and lots of
numbers closer.
So? Is *BOB* the closest number to Zero? The number that comes on the
"line" just after Zero?
Hell, no. Guess why?
Oh, yes, you are all right and you all get a virtual biscuit to go
with your virtual tea. [Which I'm not making as I find it tiring just
making my own.]
Bob isn't the closest number to Zero, even though he's closer than my
little Hunny because we can divide *BOB* by millions and millions and
millions and lots of more millions to get Gerty.
Then we can divide Gerty, who is *way* closer to Zero than Bob ever
dreamed of being, by more and more millions to make Rexy the
Wondermouse Number.
Mitch, old pal, can you see the problem?
Can you see the pattern?
We can *always divide Rexy the Wondermouse Number and all of the
littler numbers by vary, very large numbers or by two and three and
seven and sixty-six sextillion and five to make numbers even smaller,
even closer to curvy, lonely Miss Zero.
If we do all of this dividing and dividing and more dividing for
years and years and years, we get teentsy tiny numbers that make Hunny
look truly colossal.
And all of those numbers are closer to Zero than Hunny is.
Fuck "infinity", fuck "infinitesimal", we can pick *any* arbitrary
Hunny as our "number that is closest to Missy Zero", divide it as
often by as many and as large numbers as we chose to find numbers a
lot closer than is our chosen Hunny.
Now, Mitch, do you see the problem?
Post by Alan MackenzieOtherwise you just look like one more idiot on sci.math. There are
quite enough of these as it is without you adding to their number.
Are you sure we don't need more? Quarantine gets boring. We may need
new chewtoys and carloads of clowns to chastise comically.
We have to keep our minds sharp for the bright day, far in the
distant future when we beat Winnie-the-Flu to emerge onto the glorious
day lit surface of the world Man once owned.
Chewing on Mitches and Archies is also fun.
Do you understand, now? *Can* you understand?
The "Real Number Line", the "set of Real Numbers", it's continuous
and there is no "closest to Zero". Just as there is no "closest to
five" or "next number after Pi".
It's all a smoothie without lumpies and we can always cut it into
teentsier bitties.
All cool, now?
J.