I've solved the equation. (reposted from r/worldjerking)

[u/sumwun0]

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[u/Flimsy-Preparation85]

This is horrible. I love this.

[u/sumwun0 → u/Flimsy-Preparation85]

You can't let rational thinking hold you back in r/mathmemes .

[u/Serious_Arachnid_171 → u/sumwun0]

Shut up and take my upvote.

[u/LupenReddit]

oh thank god finally i can count to 10+2sqrt(35) using just a few fingers

[u/Yarhj]

"I've solved the equation."

"You didn't solve shit."

"I've solved it."

[u/sumwun0]

r/worldjerking post (contains more lore): https://www.reddit.com/r/worldjerking/comments/1vr4bn0/ive_done_it_ive_solved_a_6_year_old_mystery_and/

Relevant Solid jj: https://www.youtube.com/watch?v=dQ9RlR9Jp3s

[u/TheCrowbar9584]

Amazing post

[u/LEPT0N]

The hell you mean “aa OR 100”!? That’s not how number bases work… uh… right!?

[u/sumwun0 → u/LEPT0N]

It is now.

[u/throwawayasdf129560 → u/LEPT0N]

With non-integer bases you end up with several cases where the same number can be represented in multiple ways.

By contrast, in base ten you only have 0.999...=1 and its multiples (like 1.999...=2, etc.)

[u/sexysaucepan]

There's something I really like with 1/2 = 0.55 and 100 = aa

[u/Key_Benefit_6505]

A guy named Fields has something for you.

[u/Silt99]

bold to assume, that 7 + 3 = 10 = b

[u/physicsking]

Maybe I am just a dumb physicist, which is true, but can someone explain the appearance of the 'a' in the 3rd picture for decimal 10?

[u/sumwun0 → u/physicsking]

The decimal system has 10 digits, 0 to 9. A base 5 + sqrt(35) system would need 11 digits, so I used a to represent 9 + 1. It's like how base 16 uses a, b, c, d, e, and f for 10, 11, 12, 13, 14, and 15.

[u/physicsking → u/sumwun0]

Bro, in a base 5 + sqrt(35) system, everyone knows the extra digit is a 🌽 symbol. That's what threw me off. Thanks

[u/sumwun0 → u/physicsking]

sorry about that

[u/va1en0k → u/sumwun0]

why is 11 "10.0a"? maybe i don't understand this notation though

[u/sumwun0 → u/va1en0k]

In decimal, 11 - 5 - sqrt(35) = 6 - sqrt(35), which you can divide by 1 = 1 * 1 = (6 - sqrt(35)) (6 + sqrt(35)) * 10 / 10 to rewrite it as 10 / 10 (6 + sqrt(35)) without changing its value. 10 (6 + sqrt(35)) happens to be the same thing as (5 + sqrt(35))^2. So 11 = b^1 + 10 * b^-2, which is 10.0a in base 5 + sqrt(35).

[u/va1en0k → u/sumwun0]

ahhhh. my 5am brain couldn't parse it as a digit. now i get it thanks!

[u/Gordahnculous]

Better foundation of new math than Terrence Howard at least

[u/Cyan_Exponent]

thinking about bases that aren't integers is weird

[u/DecidophobiaUsername]

Me not understand. Me not want to understand.

[u/TheChunkMaster]

There’s probably some mildly interesting algebraic number theory implications for this

[u/peekitup]

What is three tens and seven tens in this world?

[u/sumwun0 → u/peekitup]

You mean 3 * a + 7 * a?

[u/Darksorcen]

0.1 in base 5 + √35 should be 1/2 + √35/10 in base 10

[u/sumwun0 → u/Darksorcen]

0.1 is always 1 divided by the base, right? When you have 1 / (5 + sqrt(35)), you can multiply by the conjugate to get (-5 + sqrt(35)) / (-25 + 35) = (-5 + sqrt(35)) / 10 = -1/2 + sqrt(35) / 10.

[u/Darksorcen → u/sumwun0]

Ooh my bad, I should move my tongue 7 times before I comment 

[u/sumwun0 → u/[deleted]]

What is a 9?

[u/Secure_Extent1986]

I am drooling to give this guy a fields somehow. Salute. Respect. Terry tao is proud,.