# Prove that 11111=0

Background: I am a French educated person.

My old math teacher keeps posting some small and funny riddles, here's one of his:

The next equation is correct:

11111=0

Can you prove it?

Note: Hopefully, when the answer is revealed, the tags will have been sufficient (Sorry if I missed any).

• Perhaps 1 is just a arbitrary numeric symbol that actually substitutes as 0 in this equation. Apr 18, 2018 at 16:45
• @North Well, it has been 95% solved like in an hour. I could say it's 100% solved, just waiting to see if a better explanation comes off the answerer. Apr 18, 2018 at 20:02

I'll follow the suggestion given by the OP. So:

"11111" in French reads as "onze mille cent onze", which sounds exactly as "onze mille sans onze" (11000 without 11).

Therefore we have

"000"

which comes from

"11000" without "11"

and of course

"000" means 0

Could it be that

$11111 = 11, 111$
which, in French, is pronounced "onze, cent onze".

To a speaker, this sounds very much like "onze sans t-onze" which would mean "eleven without eleven" and could justifiably be said to be zero.

NB @Maiaux has pointed out in their answer that the intention may be the whole phrase "onze mille cent onze" to sound like "onze mille sans onze" or "11000 without 11" which could be read as 000. I would say this is worth an upvote too.

• There's a French "who's on first" routine about a man ordering shirts (chemises) over the phone from a slightly deaf shop clerk. When the man is asked how many he wants, he replies: "sept" (7) "Pardon?" "J'ai dit 'sept'" (I said 7) "Ah. Dix-sept. Merci" (Oh, 17. Thanks.) "Non! Sans dix. Sept" "Cent dix-sept?" "Sept! Sans dix! Sept!" "Sept cent dix-sept?" and so on. Apr 18, 2018 at 14:20
• You're 95% right, but can you explain it using the whole number? I mean without adding a , yourself. Apr 18, 2018 at 14:21
• @PaulKaram I think I see what you mean. My French is not brilliant, unfortunately, but I will try to find a phrase that fits. Apr 18, 2018 at 14:46
• Shouldn’t it be “onze mille cent onze” in French? This sounds as “onze mille sans onze”, which could be interpreted as “mille” (1000), “11000-11=10989” or perhaps “(11-11)*1000=0”... Apr 18, 2018 at 19:32
• @hexomino In your answer, you wrote that this sounds like "onze sans t-onze", but I think the "t-" part should be removed, since, AFAIK, the "t" in "cent" is silent and there's no liaison when the following word is "onze" Apr 19, 2018 at 15:33

I would look at it from this perspective.

11111 are 5 lines.
In morse, 5 lines (dashes) means 0

• Interesting , but I am sorry, this is not the right answer. Apr 18, 2018 at 11:59
• Since we're talking about morse, how about this: The 0 represents a morse who crossed a footbridge (the =) to leave a river (the 11111). ;-)
– Alex
Apr 20, 2018 at 8:32

It might be that :

Your math teacher is also doing programming as part of his work and is using a ones' complement system. 11111 is a signed integer composed of 5 bits, which is equal to -0 in decimal which is 0, thus 11111 = 0 . See the wikipedia entry with a signed integer composed of 8 bits

The teacher asked the question "How many contours the digits on the left surround?", to which the answer is 0. For example if there was a number 8 on the left the answer would be 2.

• Not the answer. That's not visual I suppose. Apr 18, 2018 at 12:00
• And a downvote? Really? Apr 18, 2018 at 12:47
• Well, it wasn't me. And I don't really know why would it get downvoted. Apr 18, 2018 at 12:48
• @PaulKaram Well, thanks for the up-vote. It just puzzles me how negative some people could be. But, hey, it's their right to click the down-arrow. It's there for a reason. Apr 18, 2018 at 12:49
• @rhsquared I kind of welcome downvotes when they are not deserved. They attract sympathy upvotes. Apr 19, 2018 at 15:26

I remember a question like this from my Programming Teacher, i hope this isn't a duplicate from rhsquared answer, if so i am very sorry.

It looked like an equation but the Number after "=" was just the number of enclosed spaces before the "=". So 11111 has 0 enclosed spaces and 84141 for example 4 enclosed spaces

If this does not solve it, i am very excited to see the solution in the future.

11111 is in French "un un un un un", which sounds like the noise you make while shaking your head, indicating "no", or "nothing". Therefore 0.

With a little help from hexomino’s answer ;)

I think that:

‘Un onze cent onze’ (one eleven-hundred eleven) sounds like ‘un onze sans onze’, translating to ‘an eleven without eleven’, which is 0.

• How is this different from hexomino's answer? Apr 18, 2018 at 18:11
• ‘Un’ in front so there’s no need to use the comma.
– Max
Apr 18, 2018 at 18:12

A remark rather than an answer, maybe this version is a little less contorted, although slightly more dialectal:

1111 = 0 says the French teacher.

Indeed, exactly as in English you can pronounce 1111 "eleven hundred eleven", you can say "onze cent onze" in French as an alternative to "mille cent onze". Then, same as above, "onze cent onze" sounds exactly as "onze sans onze", i.e. "eleven without eleven".

Using JavaScript,

2.999999999999999999 === 3

Therefore,

11111 === 0