4 ms·
> There is no decimal expansion of 1/3. Or pi for that matter. This is incorrect. A decimal expansion is just a type of Cauchy sequence, which by definition is
by cgmg 9y ago
> There is no decimal expansion of 1/3. Or pi for that matter.
This is incorrect. A decimal expansion is just a type of Cauchy sequence, which by definition is infinite (a function from the natural numbers to the reals).
You are confusing the decimal expansion with its truncated approximations.
> If you happen to somehow built a decimal expansion of 1/3, please share it with us!
Sure thing! Here it is:
def oneThird(place):
if place >= 0:
return 0
else:
return 3
Convert to your favorite programming language/Turing machine/other abstract machine of choice.
- pacala 9y agooneThird doesn't return a decimal expansion, just one digit in a number. Still waiting for the 1 / 3 decimal expansion you claim it exists. The best I can do is: def oneThird(place): if place >= 0: return 0 else: return 3 def printOneThird(): for x in iter(int, 1): print(oneThird(-x)) Unfortunately, it didn't finish before I edited this response. Perhaps you have more patience, please let me know when you have a link to the decimal expansion of 1 / 3.
- cgmg 9y agopacala, It seems you don't understand what a sequence is. Formally, a sequence is a function whose domain is the natural numbers (or integers). A decimal expansion is simply a sequence whose codomain is the set of digits {0,1,2,3,4,5,6,7,8,9}. I gave you just such a sequence. Are you really going to continue disputing a basic mathematical fact?
- pacala 9y agohttps://math.stackexchange.com/questions/1989695/why-isnt-finitism-nonsense https://math.stackexchange.com/questions/1989695/why-isnt-fi...