Science and Technology Quiz 3

[GoodGame]

Open Floor

 

[SS-18 ICBM]

Show me how there can be a one-to-one correspondence between the set of natural numbers and the set of integers.

 

[ParadigmShifter]

Assuming 0 isn't a natural number

1->0
2->1
3->-1
4->2
5->-2

so n maps to:

0, if n = 1
n/2 if n is even
-(n-1)/2 is n is odd and > 1

similarly if you count 0 as a natural number.

EDIT: And vice versa of course to get a bijection.

 

[GoodGame]

Show me how there can be a one-to-one correspondence between the set of natural numbers and the set of integers.

If you take the absolute value of all members of the set of integers, you'll duplicate the set of natural numbers (except there will only be one "zero").

 

[SS-18 ICBM]

That was too easy, wasn't it? Your turn, ParadigmShifter.

 

[ParadigmShifter]

You mean me I presume, I'll think of one and post it tomorrow. In the meantime you can show how the rational numbers also have a 1:1 correspondence with the naturals

EDIT: GoodGame only gave a 1 way mapping

 

[SS-18 ICBM]

Just draw a grid with all the natural numbers on the horizontal axis and vertical axis, and for each cell in the grid divide the natural numbers on the axes. Draw diagonal lines showing the progression of the numbers (going through all the way to infinity), and put them in a one-to-one correspondence with the natural numbers, including the negative rationals.

Naturals/Rationals: 0/0 1/1 2/-1 3/-1 4/-1 5/2 6/-2 7/(1/2) 8/(-1/2) ...

 

[ParadigmShifter]

Yeah that's right but it isn't my proper question, more an expansion of yours I'll ask mine tomorrow.

Can you go for the encore and show why real numbers can't be put into a similar correspondence? (You can use just the interval [0,1] if you want).

 

[SS-18 ICBM]

Can you go for the encore and show why real numbers can't be put into a similar correspondence? (You can use just the interval [0,1] if you want).

Well, that's not I know how to explain it. Just come up with a list of every single real number paired with the natural numbers, and you can come up with one that isn't present in it.

If the number was the same as any one number in the list, then the one digit of it won't be different from the digit of the number in the list. There is one number that isn't in any correspondence with any natural number.

 

[ParadigmShifter]

Here is a link to the gist of the proof

http://en.wikipedia.org/wiki/Cantors_Diagonal_argument

 

[Mise]

Guys, don't make me tag this thread as 'gay'

 

[ParadigmShifter]

I'll do a short Q about computing, this will probably be easy if you google it so that is discouraged

Byte ordering of data on a computer depends on the endianness mode of the processor (big endian or little endian).

So where did the name come from originally?

 

[GoodGame]

Something to do with the size of the datablock? E.g. whether it was 8-bit or 16-bit or 32-bit, etc..

 

[SS-18 ICBM]

Guys, don't make me tag this thread as 'gay'

I don't get it.

 

[peter grimes]

I'm going to guess that it comes from the letters N and D (big endian), n and d (little endian).

But I have no guess as to why.

 

[ParadigmShifter]

All wrong answers so far

 

[GoodGame]

I'm going to guess that it comes from the letters N and D (big endian), n and d (little endian).

But I have no guess as to why.

That has me thinking about logic gates (like aND). Maybe going to assembly language programming it's like the bit of an instruction byte that applies some feature of a logic gate instruction. I'd have to search the attic for my Intel x86 assembly reference book to answer (which I won't ) .

 

[ParadigmShifter]

I'm not sure the assembly language book will have the origins of the word endian in it

Wikipedia is definitely off limits though

 

[GoodGame]

Well probably wouldn't have a detailed etymology, but I'm thinking the answer is as simple as the nickname of modifier bit on an instruction byte in assembly language.

 

[ParadigmShifter]

Nah the answer is well... different to say the least