Life Hack

You may call it an approxim8ion
- gr8 m8, I r8 8/8

you can trucate it and it still only a slightly worse approximation:
987/123 = 8.024
98/12 = 8.167
9/1 = 9.000
The last one is pretty bad you should probably not use it
- 16/2 is an almost exact replacement for 8. OP's name includes Fermat, and so he's probably smarter than me though.
- Nah, the engineer probably designed it with a safety factor. You could probably even go 9/0 and be perfectly safe ;)
  
  what about 8/1 would that be save?
- 9/1 ≈ 8
- 9/1 is approximately 8, for extremely large values of 8.
  
  Hello, fellow old nerd.
- Have you considered running for Indiana governor? You have the right mindset.
  https://en.wikipedia.org/wiki/Indiana_pi_bill
- By the way guys, a very similar approximation for 8, which also starts at 9.000 for n=1, but quickly gets much closer to 8 for increasing n, is:
  exp{-2(n-1)} + 8
  It approaches 8 about as fast as the above method but this one has a simple formula that is usable in python etc.
- For that last one, how bad are we talking? I need to know soon, I have some important banking software I need to develop.
  
  I wouldn't use it for precise calculations at NASA, but for banking stuff I think it would be fine :)
  
  It depends on the scale of the thing you're using it for.

987654312÷123456789
Change the 21 at the end of the first number to 12 and its perfect. It was only ever 9 away.
- WOOOAH🤯
- Witch! Begone foul demon, and take your dark sorcery with you!

9876543210987654321 / 1234567890123456789 = 8,0000000729000

It contains the number 8 though. So how is that useful
- It contains the numbers 8x10^{7 and 8x10}1, but not 8x10^0
- Well, simple. Jest substitute that 8 with the above approximation.

Shit like this makes me realise why people become mathematicians. You just play around with numbers and find funny facts about them.
- I myself once learned 380 digits of π, when I was a crazy high-school kid. My never-attained ambition was to reach the spot, 762 digits out in the decimal expansion, where it goes "999999", so that I could recite it out loud, come to those six 9s, and then impishly say, "and so on!"
  —Douglas Hofstadter
  
  That would be an amazing party trick.
- Then you try to figure out why they do be like that
- So, years ago in college in Linear Algebra our professor said to us to study about idempotent matrices. So I checked out that wiki page and saw the example for 2x2 matrix, that are composed by the numbers 3, -6, 1 and -2. And I was like wait a second, 3×-2=-6 there's no way they are not relationship there, so I started trying other numbers, and found and proved (using induction) that any n, -n(n-1), 1, -(n-1) is an idempotent matrix. At the test there were no questions about that, and I was short of 0.5 poits to pass the class without having to present a final exam and I told my professor that I spent a lot of time learning that and that even discovered something and proved he pass me the chart and asked me to proved it, after that he gave the missing points. Was really good.
  
  You need to put the name inside the brackets and the link inside the parentheses.
  idempotent matrices
- I mean, mathematics are an invention. A useful one, sure, but the whole thing is just made up by people playing around with numbers and going “what if we had a new, different kind of numbers…”
  
  if we play around with it and find out we can better describe how reality works it is not strictly made up
  some of it anyway and maybe all with a better understanding
  
  This reminds me of a friend who said "I like to think of dividing by zero as giving zero instead of infinity, because it means you can keep doing math on it" and I just thought that was so pure.

gonna need this in every base
I'll start with base 2:
1/1 = 1

I just noticed what the numbers are. It really is easy to memorize. So convenient.

The funniest part is that some people will never understand the absolute crusade that some mathematicians might fight over this one day

I wonder if there’s a related infinite sequence which converges on 8?
- (n * 8 + 1) / n
- This sequence approximates an integer to arbitrary precision, not 8 specifically though, and never perfectly.
  I tried it out using other bases, and the rule seems to be that doing this in base n results in n-2 with remainder n-1. So it doesn't ever actually converge, but the remainder becomes small very fast.
  
  never perfectly
  eyes you in binary

strange coincidence
- See my other comment, it's no coincide– there's a pattern. I would love to see an actual proof for it though, I don't know enough to say why it behaves that way.