Post B5LEqVUidNXxortamu by tfb@functional.cafe
 (DIR) More posts by tfb@functional.cafe
 (DIR) Post #B5Kg77IOMSNfINJYjw by hannah@hai.z0ne.social
       0 likes, 0 repeats
       
       do you ever take a short nap and your last recognisable thought is, "i need to define the number of nines in any number from 0 to 100"? because i sure did.now, it's not a real 9-counting function; it's a mathematician's 9-counting function, meaning that i want a function as nice as possible (in this case, infinitely differentiable) that does what i want in a certain circumstance
       
 (DIR) Post #B5Kgb2ZYUDJnKmbxWy by hannah@hai.z0ne.social
       0 likes, 0 repeats
       
       Spoiler: the function I defined wasf(x)=2-\frac{\log(100-y)}{\log 10}The idea is the following: the number x_k=99.9...9 with k-2 decimals is easily seen to be equal to\frac{10^{k+2}-1}{10^k}=10^2-10^{-k}(you're either a weenie like me who used geometric sums to find this or realise that x_k is a bunch of nines with a shifted decimal comma). From here, we can just writey=10^2-10^{-k} \implies k=-\log_{10}(100-y).That's exactly what we got before. Now, this is an infinitely differentiable function on y, so we just call it the 9-counting function.EDIT: see correction.
       
 (DIR) Post #B5Kggv65BzcTt4d4lc by hannah@hai.z0ne.social
       0 likes, 0 repeats
       
       The advantage of my notation is that while using grown-up log allows us to immediately define a holomorphic 9-counting function, so we can now even know the number of nines on i
       
 (DIR) Post #B5KhLx1QwLV7jM1HiS by hannah@hai.z0ne.social
       0 likes, 0 repeats
       
       OK chat sorry that procedure is rather to count the number of 9s in 0.9...9. To get the good one you need to add 2. That's because\log(100-99.9...9)=\log(100(1-0.999...9))=\log 100+\log(1-0.999...9)
       
 (DIR) Post #B5KhfHlc2GGpZUq51E by hannah@hai.z0ne.social
       0 likes, 0 repeats
       
       we now can say for certain that github has reached not 0 zeros -- but 0.993 zeros!
       
 (DIR) Post #B5KhiEiPpzRsyZkbwX by hannah@hai.z0ne.social
       0 likes, 0 repeats
       
       i am now waiting for the royalties from Microsoft for having given their marketing department some weaponry against the 0 nines non-believers.
       
 (DIR) Post #B5KhzQMzl9iG2pvYYK by hannah@hai.z0ne.social
       0 likes, 0 repeats
       
       also for fun, here's the number of 9s in the number i:-2.17136384 × 10-5 + 0.00434280006 ialso for \pi: 0.01386267638also for e:0.01196876757also for @fiore@brain.worm.pink 's constant:0.00708450298
       
 (DIR) Post #B5Kkrl7j0uNFxOozLc by fiore@brain.worm.pink
       0 likes, 1 repeats
       
       @hannah you  people  are  insane
       
 (DIR) Post #B5KksArJKYh1m1LFNA by fiore@brain.worm.pink
       0 likes, 0 repeats
       
       @hannah i love  this
       
 (DIR) Post #B5LEqVUidNXxortamu by tfb@functional.cafe
       0 likes, 1 repeats
       
       @hannah Ah yes, when I think of desirable properties of counting functions, infinitely differentiable springs immediately to mind :blobcatdizzy:Also, I'd name the function "nineage"
       
 (DIR) Post #B5LEqViXnybcVkMdKy by hannah@hai.z0ne.social
       0 likes, 0 repeats
       
       @tfb@functional.cafe i was thinking of how there is only one holomorphic function defined on most of the complex plane which has factorial-like behaviour tbh i guess continuing would have been plenty but always strive for greatness ​:wyvCool:​