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Largest calculatable number

Name: Anonymous 2007-08-28 18:58 ID:YzXI8SXh

What is the largest number that can be held in (for example) a gigabyte of memory?

Name: Anonymous 2007-08-28 19:13 ID:SR927xFN

0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

Name: Anonymous 2007-08-28 19:20 ID:j88Jh0gm

Depends on the encoding. For unsigned binary, 2^(2^33)-1.

Name: Anonymous 2007-08-29 13:55 ID:folWIKzz

The question is as vague as for example "How many letters can you write on one sheet of paper?".

Name: RedCream 2007-08-29 16:48 ID:1HdKl3oy

>>4
Pardon me, but how is the OQ vague?  A gigabyte is defined as 1024x1024x1024x8 bits, hence 233 bits.  Taking all 0s as number 0, then >>2 is correct for an unsigned binary:

2233-1
OR
28589934592-1
OR
approx. 102.6 billion

Obviously this is a profoundly enormous number.  But with a slight alteration to the encoding (like a tiny header which properly identifies the block of memory so allocated), the resulting number is still so huge that it may as well be equal to it for all practical purposes.

Name: Anonymous 2007-08-30 2:40 ID:qt7XXRwu

Because OP didn't specify anything about the number's format or encoding. Gb2 discrete mathematics.

Name: RedCream 2007-08-30 4:51 ID:UsLGIhYe

>>6
ORLY?  Can you fit a larger number into 233 bits without invoking external (and unnecessary) assumptions?

Name: Anonymous 2007-08-30 5:58 ID:qmYqlJnM

>>7
Yeah, if you use compression.

Name: Anonymous 2007-08-30 10:23 ID:uXf34WTz

>>8
Retard.
>>7
Bitches don't know about my floating point.

Name: Anonymous 2007-08-30 12:01 ID:qt7XXRwu

>>7
gb2 discrete mathematics

Name: Anonymous 2007-08-30 12:07 ID:qt7XXRwu

>>7
Ok, what if I use the first few bytes of the gigabyte to store the base of my number (as in base^exponent) and the rest of the memory stores my exponent for example. That's some huge fucking number. And not, that's not an external (and unnecessary) assumption because that's what happens on a daily basis when it comes to any kind of computational shit.

Name: RedCream 2007-08-30 23:23 ID:MJOmt6qP

>>8
A 233-bit number contains no redundancies that would allow it to be compressed.  You need to have a better sense of information theory.

>>11
OK, but the exponent is at a maximum for the base assumption, and any reduction of that exponent to create the base can't exceed
2233.  The point is, 233 bits contains a maximum of information content as already expressed by 2233, unless EXTERNAL assumptions are applied ... like any base that you'd arbitrarily choose and that is represented outside that gigabyte.  You could say that the entire gigabyte is the exponent x for the function 39328[sup]x[sup].

Name: RedCream 2007-08-30 23:28 ID:MJOmt6qP

Hmm, now I can see that what I just said was incorrect.  Let's say the gigabyte is filled entirely with 1s (as the number 0xFFF...).  That's obviously filled with redundancy.  So, it CAN be compressed, as a zipfile of it would have a header and a short segment for the encoding ("make a gigabyte of 0xFF").  I should heed my own advice.

Name: Anonymous 2007-08-31 2:33 ID:A1HhugQW

fill in up with random data. true random data doesn't compress.

Name: Anonymous 2007-08-31 7:27 ID:Heaven

entire thread is redcum sucking his own dick.

saged for the love of god.

Name: Anonymous 2007-08-31 10:50 ID:w+lah/9c

>>14
There is no true random data.

Name: Anonymous 2007-08-31 14:07 ID:Heaven

You could just use an encoding where all ones represents infinity.

Name: Anonymous 2007-08-31 20:41 ID:nICsnRXr

>>17
Go play outside, honey, while the adults talk about discrete mathematics.

Name: Anonymous 2007-08-31 21:25 ID:Heaven

>>18
Do you have any idea what you're talking about?

Name: Anonymous 2007-08-31 22:51 ID:nICsnRXr

>>19
No. Please tell me what I just typed. I'm really fucking confused.

Name: Anonymous 2007-08-31 23:22 ID:d/QXrvxW

>>16
Even "random" number generators follow algorithms.
http://en.wikipedia.org/wiki/Pseudorandom_number_generator

Although, filling it with data from a natural source (something as simple as rolling a D10 <where 10 = 0>) is possible and considered random, it would take an incalculable lenght of time.

Name: Anonymous 2007-09-01 0:14 ID:Heaven

>>20
That's what I suspected. You said something about discrete mathematics, whereas the rest of the thread was simply about mapping binary strings to concepts (numbers). Counting the binary strings would be a (rather trivial) discrete maths problem, but that's not what the OP asked about.

Name: Anonymous 2007-09-01 0:53 ID:zgbEihYU

>>22
Whereas the concept of infinity has nothing to do with discrete mathematics and thus has no place in this thread. What was your point again?

Name: Anonymous 2007-09-01 0:55 ID:zgbEihYU

>>21
Thanks for supporting my point I guess.

Name: Anonymous 2007-09-01 8:53 ID:Heaven

>>23
My point was that what the OP asked about has nothing to do with discrete mathematics. Reread >>22.

Name: Anonymous 2007-09-01 11:28 ID:zgbEihYU

>>25
Well if you think so then tell him the fucking number already.

Name: Anonymous 2007-09-01 20:33 ID:Heaven

>>26
Any number can be justified by giving a suitable encoding.

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