Biggest number

There is an upper limit to numbers. Such that when yu add 1 to it you return to zero.

You may thing this is ridculous but this has far fewer paradoxes than the concept of "infinity".

x := biggest number, ie. there does not exist y such that y > x

then spse. x+1 = 0 (as you stated above)
=> (x + 1) - 1 = 0 - 1
=> x = -1

Consider y = 0.  I think you just failed.

>>2
Your high school mathematics is no match for Horizon!

http://www.bbc.co.uk/iplayer/episode/b00qszch/Horizon_20092010_To_Infinity_and_Beyond/

>>3
Currently BBC iPlayer TV programmes are available to play in the UK only, but all BBC iPlayer Radio programmes are available to you.     Why?

You're a fucking retard, OP. If you're going to make such bold claims, you need some evidence. You've got none. Elaborate or take this shit to /x/. I would recommend working in the following order.

Claim #1: Infinity is paradoxical.
this has far fewer paradoxes than the concept of "infinity".

I'm not a math major, but to my knowledge, this is false. All I've seen is people flaunting their ignorance with "x/0 = infinity" (it isn't) and using that gem to prove that 2 + 2 = 5 or whatever.

But please, enlighten me. Demonstrate or explain at least one paradox of infinity.

Claim #2:
There is an upper limit to numbers.
How did you reach this conclusion? Do you have a formal proof? What is this limit, is it calculable?

Claim #3: Numbers overflow to zero after this proposed upper limit.
>when yu add 1 to it you return to zero.

(This make me suspect you just got out of a CS101 class or something. What, did you just learn about fixed-legth registers and arithmetic overflow?)

Again, no evidence and no formal proof. Please demonstrate a known case that satisfies "x + 1 = 0; where x > 0".


Other thougts:

a) If "x" is the "upper limit to numbers", does that mean "-x" is the limit on negative numbers? Is "1/x" the limit on small numbers? What about imaginary numbers and other number systems? Do these all overflow to zero as well?

b) What is the value of "2x"? "x - 1"?

>>4
Download it from piratebay.

>>5

You're a fucking retard, OP

Now then, now then, there's no need to resort to a beliggerant attitude as if you are from imageboards because an idea is new so drop the ad homs.

Demonstrate or explain at least one paradox of infinity.

There are several.

For example : Infinity take away Infinity can be zero but it can also be anything else. Normally, x - x = 0 xEr

Any sub set of infinity can be larger than infinity.

And there are many more you can find using your favourite search engine.

There is an upper limit to numbers.

This is because of the paradoxes of infinity.

Claim #3: Numbers overflow to zero after this proposed upper limit.

This is a logical deduction of claim 2.

These are not my ideas, rather the ideas of well respected mathematicians.

I do not know the answers of a) and b) but that does not mean I won't sometime in the future. =]

>>6
FAIL
Now then, now then, there's no need to resort to a beliggerant attitude as if you are from imageboards because an idea is new so drop the ad homs.
It wasn't ad hominem. It was simple insult. http://en.wikipedia.org/wiki/Ad_hominem#Common_misconceptions_about_ad_hominem

I didn't call you a retard because the idea is new. I called you a retard because you're talking out your ass just like all the other retards I mentioned.

Infinity take away Infinity can be zero but it can also be anything else.
You've just proven me correct, you're flaunting your ignorance. Infinity is not a simple number. It is an unbounded limit that must be defined. Without definition, infinity minus infinity is undefined. HURR DURR, big shock.

Any sub set of infinity can be larger than infinity.
This is a concept called cardinality. It is not a paradox because infinity is not a number.

And there are many more you can find using your favourite search engine.
LOL. And you're accusing ME of fallacy?

This is because of the paradoxes of infinity.
I'll ask you again to provide one. Then, if you'd like to avoid another non sequitur, you need to show how that supports your claim. Even if infinity were flawed, that doesn't lend your baseless claims any weight.

This is a logical deduction of claim 2.
Claim 2 hasn't been established as true. And claim 3 does not follow directly from claim 2. Why overflow to zero and not, say 150,334? Why overflow at all?

These are not my ideas, rather the ideas of well respected mathematicians.
So now you're trying an appeal to authority? Citation fucking needed or GTFO.

While there are a (very) few serious mathematicians who do not believe the concept of infinity should be used (see, for example, finitism: http://en.wikipedia.org/wiki/Finitism), I don't believe that any of them would ever consider adopting your absurd solution.

The Archimedean property (proven from the completeness of the real line, which in turn can be proven in ZFC which is generally considered standard) asserts that for any real number x, there exists a natural number n such that x < n.  If we use your crazy system, we cannot have any sort of ordering on the naturals because if we take your upper limit, say x, the natural number y greater than it must then satisfy y < x < y, which is a contradiction.

tl;dr pretending the naturals are actually the integers modulo n for an "upper limit" n doesn't really make the natural numbers go away.

Who knows what is biggest number all I know is 1 is the loneliest number.

Who hates it

Troll troll is a troll based on an appallingly misinformed Horizon episode. However, it should be noted that even "finitists" believe that there is no largest natural number. I've no idea how they found that crazy guy, and although he's a Professor (in the American sense) it doesn't say he's a mathematician - still, this does teach you not to expect too much from a university like Rutgers.

To clarify it wasn't a troll I just wanted some discussion on infinity however misguided that was...

The number is 65535.  ez

How familiar are you with the field of very large numbers?
http://en.wikipedia.org/wiki/Large_numbers

Anyone can easily represent "one million" on paper, simply by writting out "1,000,000". It is only 7 digits with optional separaters for clarity. In everyday terms, that is a big number. With a million dollars, you could live your entire life in carefully measured comfort. Add a few more digits, and with a billion dollars you could do practically anything you wish for the rest of your life... and still have money to burn. Add a few more digits, and with a trillion dollars, you could make a significant global impact. 1,000,000,000,000 is still a very small number.

Ask a school child (or even most adults) what the largest number they can name is and most will say "a googol" or "a googolplex" (now often confused with the famous internet search engine, spelled differently). One million is 10⁶. A googol is 10¹⁰⁰ (or 10¹⁰²). It is a one followed by 100 zeroes; a 101-digit number. You could again easily write this down on a sheet of paper, but it would be a bit tedious:

1 googol = 10¹⁰⁰ = 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

There are roughly 10⁸⁰ atoms in the Universe. That means you would need to count every atom in existence 100,000,000,000,000,000,000 (10²⁰) times over to reach 1 googol. That's a pretty big number, but you only need 101 digits to represent it.

But a googolplex is on another scale entirely. 1 googolplex is 10^googol (10¹⁰¹⁰⁰); it is a number with "a googol + 1" digits. You couldn't write out that many zeroes with all the paper on Earth.

As I said, there are only 10⁸⁰ atoms in the Universe. 10¹⁰⁰ digits and only 10⁸⁰ atoms to work with. See the problem?

Assuming each digit requires one byte to encode, a modern 1 TB hard drive would be filled with a single trillion-digit number (10¹² digits). That means that you would need a hundred million (10⁸) of those hard drives for every atom in the Universe in order to store a googol zeroes. Yeah. Not possible. We can only reasonably represent it using exponents: 10¹⁰¹⁰⁰.

But even a googolplex is tiny when compared to other large numbers.

Take, for example, the Busy Beaver function.
http://en.wikipedia.org/wiki/Busy_beaver

The result of the Busy Beaver Σ function grows so fast, we've only been able to calculate a 2-symbol BB Σ(n) for n=1, n=2, n=3, and n=4.

BB Σ(1) = 1
BB Σ(2) = 4
BB Σ(3) = 6
BB Σ(4) = 13

Beyond that point, we've only been able to estimate very loose lower bounds for what the actual value is. We simply do not have the resources to calculate the actual values.

BB Σ(5) has been calculated to be at least 4098 and BB Σ(6) is at least 4.6 × 10¹⁴³⁹. They are likely much larger.

BB Σ(7) is said to be easily large enough to put googolplex to shame.

The result of BB Σ(8) is likewise said to be so large as to be physically impossible to represent at all, not with exponents, not even using Knuth's notation.
http://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation

So what happens when you get serious with this function?

How could we possibly work with a number like BB Σ(100)? Or BB Σ(googolplex)?

What happens when you start manipulating the function itself?
You could add to it: BB Σ(100) + 100
You could multiply by it:　100 x BB Σ(100)
You could use it as an exponent: 100^{BB Σ(100)}

Or, thinking bigger, you could exponentiate the function by itself: BB Σ(100)^{BB Σ(100)}
Or use Knuth's notation: BB Σ(100) "↑"↑"↑"↑ BB Σ(100)
Or even: BB Σ(100) ↑^{BB Σ(100)} BB Σ(100)

But even that's nothing compared to nesting the function within itself: BB Σ(BB Σ(100))
Using a greater number of symbols would also explode the values monstrously.


All of these can be easily written down, but represent numbers so large as to be completely meaningless. We have absolutely no practical need for such numbers. Yet no matter how high we go, we can easily go higher.

The concept of a "biggest number" is untenable and frankly absurd. There is no evidence to even suggest its existence. On the contrary, it is quite simple to disprove, as has already been done in this thread. It would, by definition, be at the end of the numberline, which would be like saying "0.000...1", which simply doesn't make sense and is a common troll theme.

>>13
Did you have fun pretending you were Carl Sagan for the majority of that?

Assign arbitrary identifier to arbitrarily large number
Revel in amazement1

I wonder. If the universe we lived in had been `noticably curved', i.e., the effect was clear even on small drawings, would we ever have invented plane geometry? Maybe we'd think of it as a really weird and abstract special case of a generalization.

"The good Christian should beware of mathematicians and
all those who
make empty prophecies.  The danger already exists that
mathematicians
have made a covenant with the devil to darken the spirit and confine
man in the bonds of Hell." -- St. Augustine (354-430)

Babbage, Charles (1792-1871, English mathematician and inventor of
computer)
On two occasions I have been asked [by members of Parliament], 'Pray,
Mr.
Babbage, if you put into the machine wrong figures, will the right
answers
come out?' I am not able rightly to apprehend the kind of confusion of
ideas that could provoke such a question.

"A mathematician is a blind man in a dark room looking for a black
cat
which isn't there" - Charles R. Darwin (1809-1882)

Math is like love -- a simple idea but it can get complicated.

Mathematicians are like lovers. Grant a mathematician the least
principle, and he will draw from it a consequence which you must also
grant him, and from this consequence another.
-- Bernard Le Bouyer Fontenelle

"The laws of probability, so true in general, so fallacious in
particular."
 -- Edward Gibbon (1737-1794)

Thomas Godfrey, a self-taught mathematician, great in his way . . .
knew
little out of his way, and was not a pleasing companion; as, like most
great mathematicians I have met with, he expected universal precision in
everything said, or was forever denying or distinguishing upon trifles,
to
the disturbance of all conversation. --Benjamin Franklin (1706-1790),

Halmos, Paul R.
I remember one occasion when I tried to add a little seasoning to a
review,
but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a
perfectly sound contribution to abstract measure theory. The domains of
the
underlying measures were not sets but elements of more general Boolean
algebras, and their range consisted not of positive numbers but of
certain
abstract equivalence classes. My proposed first sentence was:
"The author discusses valueless measures in pointless spaces."

Hempel, Carl G.
...to characterize the import of pure geometry, we might use the
standard
form of a movie-disclaimer: No portrayal of the characteristics of
geometrical figures or of the spatial properties of relationships of
actual
bodies is intended, and any similarities between the primitive concepts
and
their customary geometrical connotations are purely coincidental.

Stand firm in your refusal to remain conscious during algebra.  In
real
life, I assure you, there is no such thing as algebra"
  -- Fran Lebowitz

Mathematics is inadequate to describe the universe, since mathematics is
an
abstraction from natural phenomena.  Also, mathematics may predict
things
which don't exist, or are impossible in nature.
 -- Ludovico delle Colombe Criticizing Galileo.

Mathematics is as little a science as grammar is a language.
  -- Ernst Mayr

>>13
You couldn't write out that many zeroes with all the paper on Earth.
What if I wrote the 0's really small?

>>18

Yeah, seems like the "scientists" always overlook such easy refutations when they make these ridiculous claims. I bet many of their theories which we don't understand, are based on similarly flawed logic.

>>18-19
Numbers are infinite, so it doesn't matter how "small" you write the "0s", Earth will eventually run out of its resource of paper.

HIBT?

>>19
I really, really hope you're joking. Please, come on. Tell me you're kidding. You know you can't be THAT subtle around here. Poe's Law and all that.

>>13
This post did not deserve this quality of a response, but I thank you for it all the same.

I am knowing sorry not knowing what s the biggest number in the world but I do know that one is the loneliest number that youll every know. 2 I think can be just as lonely unless its big blzck penis night for your gf willhave hella woot fun.