- #1

- 5

- 0

Would the amount of shapes/objects in this cube be infinite? (Assuming the black pixels represent solids)

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter question99
- Start date

- #1

- 5

- 0

Would the amount of shapes/objects in this cube be infinite? (Assuming the black pixels represent solids)

- #2

- 18,306

- 11,561

You have posited a finite number of things. How would you get from finite to infinite?

Would the amount of shapes/objects in this cube be infinite? (Assuming the black pixels represent solids)

- #3

- 23

- 0

This is their total possible combinations as a cube but also as a string, so this is the total possible combinations for any shape and as you could arrange it into an infinite number of shapes in space. The combinations of shape would be infinite, but the permutations would be finite.

- #4

- 23

- 0

Sorry I got it wrong, for my example of a 4x4x4 it would be^{64}P_{32}=4.822199248906x10^{53}total possible combinations. This would be bigger with a billion^{3}pixels.

This is their total possible combinations as a cube but also as a string, so this is the total possible combinations for any shape and as you could arrange it into an infinite number of shapes in space. The combinations of shape would be infinite, but the permutations would be finite.

- #5

Science Advisor

- 2,813

- 491

- #6

- 399

- 119

For a set of 2N items, the number of subsets of size N is called _{2N}C_{2} ("2N choose 2") and is exactly equal to (2N!)/(N!)^2.

Stirling's approximation to K! is

This gives

_{2N}C_{2} ~ √(4πN) (2N)^{2N} e^{-2N} / (√(2πN) N^{N} e^{-N})^{2}

which simplifies to

For N = 10^{9}, this is approximately 3.7965 × 10^{602,059,986}.

(Some calculators will say this is infinity.)

Stirling's approximation to K! is

K! ~ √(2πK) K^{K} e^{-K}.

This gives

which simplifies to

2^{2N} / √(πN).

For N = 10

(Some calculators will say this is infinity.)

Last edited:

Share:

- Replies
- 6

- Views
- 559

- Replies
- 1

- Views
- 543

- Replies
- 9

- Views
- 577

- Replies
- 0

- Views
- 508

- Replies
- 2

- Views
- 492

- Replies
- 6

- Views
- 557

- Replies
- 1

- Views
- 517

- Replies
- 45

- Views
- 523

- Replies
- 3

- Views
- 722

- Replies
- 3

- Views
- 2K