General > General Technical Chat

Rational, Irrational, and Integer. The correct definition.

<< < (12/12)

EPAIII:
Yea, yea, yea! And the earth is flat. And the moon landings never happened. And ...




--- Quote from: Peter Taylor on December 21, 2022, 03:43:02 am ---This is the new and correct definition of a number.
1/ A number must be an integer.
2/ The term rational and irrational don't apply to a number by definition 1/.

An integer is any number that can be defined wholly. For instance, 7, and 1 / 7 can be defined wholly and are therefor integers.
An equation that cannot be defined wholly, such as root 2, where we don't know what number multiplied by itself equals 2, remains a question, and is not a number by definition 1/.
A number can't be rational or irrational. These terms have no meaning.

Thankyou.  :D

--- End quote ---

SiliconWizard:
Some food for thought for anyone interested. (Some people call that education, but maybe saying this is oppressive now, so I dunno.)



Circlotron:

--- Quote from: Nominal Animal on December 23, 2022, 12:51:46 am ---
--- Quote from: TimFox on December 22, 2022, 08:13:50 pm ---There is a whole lot more data extant than the extent of the universe.  There are unreliable estimates of the data content of the holdings (digitized or not) of the Library of Congress, but they range up to the petabytes, or roughly 253 bits.
--- End quote ---
Yup, I only meant to illustrate how little data one can encode in a single length.

If I try to consider how much information the universe contains, I get genuinely scared/overwhelmed.  :-[

For illustration, consider a cubic meter of iron, about 7874 kg, containing about 8.5×1028 ≃ 296 iron atoms.  Iron has four stable isotopes, so in theory we could encode two bits per atom just by selecting the isotope, so that cubic meter of iron would then encode 297 bits of information.

How much is that? Well, if you unraveled that cubic meter into a monomolecular thread, just one atom wide, and you could read it at light speed, your bandwidth would be about 262 bits per second, some 500 Libraries of Congress per second.  It would take about 1088 years to read the entire iron cube.

About 30% of Earth is iron, or about 269 cubic meters of it.  That's just on Earth, mind you.  Since iron is the end product of both fusion and fission chains, there is a lot of it in the universe.  And this is just a single information storage method with zero compression, just picking between four well-known stable iron isotopes.  There are much more dense methods; I just picked iron because it is utterly stable, easy to grasp, and Stephen Baxter wrote a story about it.

--- End quote ---

Looks like Big Iron, the euphemism for large scale computer hardware, has been redefined.  :)

Navigation

[0] Message Index

[*] Previous page

There was an error while thanking
Thanking...
Go to full version
Powered by SMFPacks Advanced Attachments Uploader Mod