complex expression that gives 1 [closed]

What is the most complex(meaning complicated not meaning complex numbers or variables ) expression in Math that gives 1. An expression using all the math you know of and then make it as complex as you can

closed as too broad by Austin Mohr, Eric Wofsey, Marconius, user99914, Joel Reyes NocheOct 20 '15 at 0:59

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.

• Why get into that trouble? Is there any specific reason? What purpose does it serve? – thanasissdr Oct 20 '15 at 0:11
• I'm sorry that people have been downvoting your question but no one has told you why. Your question doesn't seem well formulated. To me, I can't understand it unless you tell me what you mean by the word complex. And even then, how do you judge an expression's complexity? These are issues that need to be addressed clearly for your question to make sense. – layman Oct 20 '15 at 0:13
• how far would you go to make an expression like it?it can serve as a new topic to discuss and many more – Ramu Oct 20 '15 at 0:13
• @user46944 complex meaning just a random expression which is complicated not adressing complex numbers or variables – Ramu Oct 20 '15 at 0:15
• @ramu But what does complicated mean? Do you mean cluttered instead? Do you want something that superficially looks highly technical, but can really be simply reduced? That's what the answer already posted does. – layman Oct 20 '15 at 0:16

Let $a$ be the most complex valid expression equal to one. consider $b:=\sqrt{\frac{a+1}{\sum_{i=0}^{\infty}2^{-i}}}$ clearly $b$ is more complex than $a$. thus such an expression can not exist :-)
• @5xum I don't see how $b$ here is "complicated" -- whatever that means. The answerer wrote the square root of a fraction where the numerator is the sum of $1$ and a representation of $1$, and the denominator is a representation of $2$. – layman Oct 20 '15 at 0:18
• @user46944 That's the whole point. If $a$ is a complicated expression that represents $1$, then $b$ is also an expression that represents $1$, and it is more complicated than $a$. "Complicated" is not a strict mathematical term, but it looks like most people agree that the more things in the expression, the more complicated the expression. – 5xum Oct 20 '15 at 0:20