Peck by twetch#2936

1F1ZT6…S6ix Key · twetch

One of the ways to answer 0!=1 in math is by "completing the pattern" (4!=5!/5, 3!=4!/4... 0!=1!/1) but if you complete the pattern in the opposite direction going from negative numbers(-4!= -5!/5, -3!=-4!/4)... 0! = -1?
Is this incompleteness?

twetch#21877 6.4y

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Transaction: 7f7785c728a9d99b0fa9b22730dfdc331e483516bbb416634f6157119585a038
Block: 634 712
Time: 2020-05-13T05:56:40Z
Signer: 1F1ZT6VXT4LCQcg13Tdp7x99zzoSQLS6ix
App: twetch
Type: post
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References: e576a2f5dcbcdf03a2dbf94f02ec227881f417bc123fdfaf81d9d1b42f2ea032
Name in tx: twetch#2936

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Replies (4)

twetch#21877 6.4y

16SgJC…e6WS Key · twetch

Replying to@1F1ZT6…S6ix

Yeah, not so sure about that. The factorial is defined on positive integers by induction. What value to assign the base case of 0 is in a sense a free choice, but you know you'll always want 0!=1 for binomial theorem, etc...

twetch#21877 6.4y

16SgJC…e6WS Key · twetch

Replying to@16SgJC…e6WS

As it turns out, of the countably many continuous extensions of factorial to C, there is a unique meromorphic log convex one called the gamma function, but even she has poles at all negative integers. There really is a problem with thinking -1!=0!/0.

twetch#2936 6.4y

1F1ZT6…S6ix Key · twetch

Replying to@16SgJC…e6WS

Thanks for the clarification, I need to read up on my definitions! I'm no mathematician by any means but i do find philosophy of mathematics very interesting.

twetch#21877 6.4y

16SgJC…e6WS Key · twetch

Replying to@1F1ZT6…S6ix

I would certainly agree. I strongly recommend the book Proofs and Refutations by Imre Lakatos if you haven't read it. It's rather accessible and a gem!

Post by twetch#2936

Replies (4)