5
$\begingroup$

You are provided with the 8-segment array in the picture together with all the necessary electronics to make any combination of lit segments you want.

enter image description here

Fillable version for graphics. http://i.stack.imgur.com/K1hnN.png

enter image description here

What is the smallest positive number that you can display without any two boxes being identical? (A box is a grey rectangle containing 8 segments)

Any combination of segments is allowed within a box provided it is accepted by the community as a valid symbol. ('accepted' is decided by net up-votes for your answer)

Any recognised numbering system that is commonly used is allowed. If the one you use is common but little-known (perhaps because it is specialized) then you must back up your claim with a link to an authoritative source. You must also explain it precisely so that it can be understood by others.

You cannot mix numbering systems unless you can show that this is routinely done by some substantial section of the populace.

You cannot invent your own symbols or language. All symbols must be understandable and approved by the community.

The competition remains open until there has been no answer for one week. At that point (or as soon after as I am able) I shall accept the most up-voted answer (net votes).

Update

  1. The question has been put on hold--therefore I'll make an adjustment about the timescale for accepting an answer (if you want to reopen it please vote to do so).

  2. If I could wind back the clock, I would require the answers to be finite. This was an oversight because I did not think an infinite could be considered a number.

  3. Because there are answers and they have been voted on, it is too late to change the criteria. My suggestion is that people who are interested submit answers in the categories of finite or infinite numbers according to their preference. I will stick to my original criterion for acceptance. Note

You can display your answer using ASCII provided it is clear how it would look when translated into segments. Otherwise please use an actual 8-segment representation to clarify the layout of any symbols that aren't obvious.

$\endgroup$

closed as too broad by Deusovi, Aggie Kidd, Milo Brandt, f'', xnor Oct 30 '15 at 20:46

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 1
    $\begingroup$ Most upvoted answer is almost certainly not going to be the "correct" answer. Your scoring condition makes this not a puzzle. $\endgroup$ – Deusovi Oct 30 '15 at 13:14
  • $\begingroup$ @Deusovi, What scoring system do you suggest? $\endgroup$ – chasly from UK Oct 30 '15 at 13:17
  • $\begingroup$ Smallest valid answer, where validity is determined either by strict rules or, if necessary, positive score. $\endgroup$ – Deusovi Oct 30 '15 at 13:25
  • $\begingroup$ It's too late for me to change it now. However, if you have an idea for a similar question but with your rules please feel free to post it. P.S. My motivation is to find numerical problems that can't be tackled by computer or brute force.. $\endgroup$ – chasly from UK Oct 30 '15 at 13:27
  • $\begingroup$ It's an interesting problem, but "satisfy other people" is what the scoring system essentially boils down to, and the problem itself seems poorly defined. $\endgroup$ – Deusovi Oct 30 '15 at 13:44
22
$\begingroup$

I don't know if you can get smaller than

enter image description here

epsilon - a small positive infinitesimal quantity

$\endgroup$
  • $\begingroup$ Also possible is: "DEN" for "denormalized number". Not seen on any calculators that I know of, but I've never seen one that displays "EPSILON" either. Commonly used in some programming languages to represent a number too small to be programmatically distinguishable from zero, but specifically NOT zero. $\endgroup$ – Darrel Hoffman Oct 30 '15 at 13:44
  • $\begingroup$ @DarrelHoffman DEN is too short though $\endgroup$ – DrunkWolf Oct 30 '15 at 13:46
  • $\begingroup$ VS C++ (don't know about other languages/compilers) usually shows DEN with a couple of digits after it, so "DEN0.1234" maybe? $\endgroup$ – Darrel Hoffman Oct 30 '15 at 14:00
10
$\begingroup$

Here's one to start off: 1 E - 9 8 7 6 5 $=10^{-98765}$

$\endgroup$
  • $\begingroup$ You may want to drop the 1 in front of the E, and instead improve the exponent. See for instance stackoverflow.com/questions/10687016/…. $\endgroup$ – Gamow Oct 30 '15 at 8:33
  • 3
    $\begingroup$ @Gamow In my opinion, the E[number] is shorthand for a multiplier, and it's not a well-formed number without something in front of it. $\endgroup$ – f'' Oct 30 '15 at 12:22
  • $\begingroup$ I am not sure if the order of operations will be executed correctly, but I think this '1E-7^998' (using different ways of representing a 9) will be smaller. $\endgroup$ – fibonatic Nov 2 '15 at 15:27
7
$\begingroup$

Building up on f'' s answer:

        ###           ###    ###    ###    ###    ###
    #  #             #   #  #   #  #   #      #  #
    #  #             #   #  #   #  #   #      #  #
    #  #             #   #  #   #  #   #      #  #
        ###    ###    ###    ###    ###           ###
    #  #                 #      #  #   #      #  #   #
    #  #                 #      #  #   #      #  #   #
    #  #                 #      #  #   #      #  #   #
        ###           ###           ###           ###

$=10^{-99876}$

Using the possibility to write the digit 9 in two different ways on this kind of display.


Edit:

Dropping the 1 in front we could get as low as $10^{-998766}$:

 ###           ###    ###    ###    ###    ###
#             #   #  #   #  #   #      #  #      #
#             #   #  #   #  #   #      #  #      #
#             #   #  #   #  #   #      #  #      #
 ###    ###    ###    ###    ###           ###    ###
#                 #      #  #   #      #  #   #  #   #
#                 #      #  #   #      #  #   #  #   #
#                 #      #  #   #      #  #   #  #   #
 ###           ###           ###           ###    ###
$\endgroup$
  • $\begingroup$ As with Gamow's comment to f", you can use this to get E-998765, which I would accept $\endgroup$ – Ross Millikan Oct 30 '15 at 8:42
  • 4
    $\begingroup$ I don't think a leading E is widely interpreted as a number. It's certainly not one in C syntax that's widely used as-is or slightly adapted for other languages. $\endgroup$ – R.. Oct 30 '15 at 15:55
  • $\begingroup$ You could also use an alternative for 7. $\endgroup$ – fibonatic Nov 2 '15 at 15:12
3
$\begingroup$

In non-standard analysis, a halo (or monad) is described as "the collection hal(x) of numbers which are infinitely close to x " (Lobry et al). Thus, the numbers close to 0 would be hal(0) or monad(0). Hyperreal numbers are described further in "Foundations of Infinitesimal Calculus" (Keisler)

       _            _   _      _
| |   | |   |      |   | |      |
|-|   |-|   |      |   | |      |
| |   | |   |_     |_  |_|   . _|

References:

Keisler, H. Jerome. Foundations of infinitesimal calculus. Vol. 20. Boston: Prindle, Weber & Schmidt, 1976.

Lobry, Claude, and Tewfik Sari. "Non-standard analysis and representation of reality." International Journal of Control 81.3 (2008): 519-536.

$\endgroup$
  • $\begingroup$ This has 2 boxes identical (empty) $\endgroup$ – DrunkWolf Oct 30 '15 at 13:45
  • $\begingroup$ @DrunkWolf fixed $\endgroup$ – user2674 Oct 30 '15 at 14:17
  • $\begingroup$ Is that really a number or is it a set of numbers? $\endgroup$ – Bodo Thiesen Oct 30 '15 at 17:16
3
$\begingroup$

What about

this.
Using Hex, that's A^-FEDCB

Equivalent to 10^-1043915

$\endgroup$
  • 1
    $\begingroup$ I think you need lower-case 'd' or call it zero. $\endgroup$ – chasly from UK Oct 30 '15 at 18:57
  • 1
    $\begingroup$ Also if that is B, then what would 8 be? $\endgroup$ – RemcoGerlich Oct 30 '15 at 20:07
0
$\begingroup$

Here's my attempt:

enter image description here

Probably not a valid solution though since it is actually not positive.

$\endgroup$
  • 1
    $\begingroup$ That's exactly 0. $\endgroup$ – Deusovi Oct 30 '15 at 10:24
  • $\begingroup$ Yes, that's why I wrote it's not positive. And the more I thought about it after posting it, the sillier it seemed, since it could just as well have said 1-1! $\endgroup$ – Petter Oct 30 '15 at 10:30
  • $\begingroup$ What about 1 - 0.988... or 1 - 0.911... Do all repeating decimal digits round up? $\endgroup$ – chasly from UK Oct 30 '15 at 12:11
  • 1
    $\begingroup$ 1 - 0.988... would be equal to 0.111..., and 1 - 0.9111... would equal 0.088888, they would be positive, but not very small :) $\endgroup$ – Petter Oct 30 '15 at 12:49
  • 8
    $\begingroup$ Lots of duplicate boxes as well in this one $\endgroup$ – DrunkWolf Oct 30 '15 at 13:47
0
$\begingroup$

What about...

1 / treE(3)

I think you can do a divide sign...

$\endgroup$
  • 1
    $\begingroup$ Can you show how this can be done with the LEDs? $\endgroup$ – Ric Oct 30 '15 at 18:45
  • $\begingroup$ center, top right, and bottom left segment could be a passable slash. Not sure what t looks like, though. $\endgroup$ – Random832 Oct 30 '15 at 18:56
  • $\begingroup$ Top-left, center, bottom-left and bottom $\endgroup$ – KingErroneous Oct 30 '15 at 20:36

Not the answer you're looking for? Browse other questions tagged or ask your own question.