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I am gonna to Introduce the brace function! click the link! 

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Introducing brace function! It can be written as Brace(n) or brace(n)   , the only diff is caps, no case sensitive. And for now, i shall use the comma (,) as followed by. \(a\)

History

First brace.JPG

I discovered it, using the braces.

When i tried to make many epsilon stack, then i make many braces that is ("this amount of") epsilons. Then "this amount of this amount of". And i made "this amount of this amount of this amount of".... I wrote it in about march or april 2013. Then... I try it on finite thingy. And i wrote the different amount of entries, with the different properties. So then, i started creating it.

Rules

  1. if the slash was used, there can be only one and after the first number. And it will be n.5 entries.
  2. Brace(@,1) ≠ Brace(@) (not confirmed)

Target

\(\omega\)

One entry (below 2 entries)

  • Brace(0) = ?, it is 0 followed by 0 for 0 times!
  • Brace(1) = 1
  • Brace(2) = 22
  • Brace(3) = 333, because, \(\underbrace{333}_{3}\). I use braces.
  • Brace(4) = 4444

Growth: >ƒ2, for 1.0 entry and 1.5 entries too.

Factorials

  • Brace(3!) = (3!),(3!),...,(3!) with 3! 3!'s or 6,6,6,6,6,6 = 666666. \(∵\) 3! = 1 × 2 × 3 = 6. = Brace((3)!)
  • Brace(3)! = 333! = (Brace(3))!

More than one digits

Yes, is still followed by.

  • Brace(11) = 1111111111111111111111. Is 11 followed by 11 for 11 times including the first 11.
  • Brace(123) =  \(\underbrace{123123123 \cdots 123123}_{123~123's}\) lol, i use BRACES and thats why i named brace function.

Nested (one entry)

Nested could be confusing to solve.

  • Brace(brace(2)) = (brace(2)),(brace(2)),(brace(2)),...,(brace(2)),(brace(2)). With brace(2) brace(2)'s
    or 22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22, 22 pairs of 22 (because brace(2) is 22.)

1.5 entries.

I shall use the comma to indicate "followed by".

Brace(a/b) = \(\underbrace{a,a,a, \cdots ,a,a,a}_{b~a's}\).

  • Brace(0/1) = 0
  • Brace(0/2) = 00 , lol, it is still the same answer as brace(0/1).
  • Brace(1/0) = AHH

With the slash, it will be n.5 entries.


Two entries (type 2) NOT CONFIRMED YET

Brace(a,b) the real 2 entries!

c is hyper operator... means c = 1,2,3,4,5... is +,×,^,^^,^^^...

So,

Brace(a) = a,a,...,a with a a's

Brace(a,b) = ababab...baba.

And Brace(a/b,c) = acacac...cacaca with b a's.

If the last entry is 1: Brace(a/b,1) ≠ brace(a/b)... maybe

Two entries (type 3) (type 1 + type 2)

Brace(a,b/c) = \(\underbrace{acacac \cdots cacaca}_{b~ac's}\). or \(\underbrace{a\{c\}a\{c\}a\{c\} \cdots \{c\}a\{c\}a\{c\}a}_{b~a\{c\}'s}\) using the bowers bracket operator in the old version.

LOL!!!


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