Title text:
Other numbers are largely unaffected, but anyone using ‘4’ for their certificate key is urged to upgrade to ‘5’.
Transcript:
Transcript will show once it’s been added to explainxkcd.com
Source: https://xkcd.com/3314/
Title text:
Other numbers are largely unaffected, but anyone using ‘4’ for their certificate key is urged to upgrade to ‘5’.
Transcript:
Transcript will show once it’s been added to explainxkcd.com
Source: https://xkcd.com/3314/
Reinventing church numerals as a rationalisation for grocery checkout hijinks - I absolutely love this.
I guess if I say that 1 is baker’s 0, and 2 is baker’s baker’s 0, then I’ve invented the baker’s unary base.
Isn’t this Peano numerals? Church numerals would be if a baker’s four doubled two was sixty-four.
(That being (λf. λx. f (f (f (f (f x))))) (λn. λf. λx. n f (n f x)) (λf. λx. f (f x)))
Would they not be equivalent systems for this purpose? Both use the successor function as a unary representation of the natural numbers.
Yes, Church numerals are something more specific. Church numerals are a model of Peano arithmetic, I think. So basically all Chuch is Peano but not all Peano is Church.
Ohhh, I see what’s happened!
Okay so, in this case you could make an argument that these aren’t Peano numbers because this isn’t an operation involving the set of all natural numbers (as in this hypothetical we’re starting from 10, not 0) nor are they church numerals (as a term for a unary representation) for the same reason (and also they aren’t for the other use of church numeral as the count of repeated composition [edit: and I will yoink that sidetrack ramble. bad warl0k3]), but I’m not going to do that because fuck me would that be a sign of near-terminal grass deficiency. Anyway, the above method of rationalizing grocery crimes is an example of what in computer science is generally called a church numeral, but only when working within a context that assumes base-10 representations of values are a shorthand for a unary representation of values. Whereas what generally gets called ‘Peano numbers’ are a purely unary expression of the natural numbers, but does not need the additional context to specify their use in this manner. I was assuming that compsci context, which I realize now that I shouldn’t have been doing
Thank you, this was interesting and something I really should have been more aware of!