10,824 Pages

# Bubby3

## aka Matthew

My favorite wikis
• I live in Mason, OH
• I was born on February 17
• My occupation is Nothing
• I am Male
• ## Church Kleene ordinal question

August 10, 2017 by Bubby3

$$\omega^{CK}_1$$ is the ordinal strength of Turing Machines, and the smallest non-recursive ordinal. What about $$\omega^{CK}_2$$ or $$\omega^{CK}_n$$? If $$\omega^{CK}_1$$ is the limit of A(0), B(0), C(0), D(0), and so on, where A, B, C, D... are normal functions, is the limit of $$A(\omega^{CK}_1+1)$$, $$B(\omega^{CK}_1+1)$$, $$C(\omega^{CK}_1+1)$$, $$D(\omega^{CK}_1+1)$$... $$\omega^{CK}_2$$ or it is smaller. Also is the limit of oracle machines with access to the halting problem $$\omega^{CK}_2$$?

• ## I dislike it when articles or blog posts have several empty sections at the end

August 8, 2017 by Bubby3

When I know an article has a lot of sections, I get excited for the content it has, only to click on the section, and to find nothing there. I then get disappointed at the fact that there is not content in the section, and want to add more to it. I feel like I am getting ripped off by the person who made the empty sections, and get impatient for them to add the content in.

Also, I don't like "Coming soon" tags placed in articles, I don't know when the content is coming out. It come out tomorrow, in a few years, or never, and most of the time it is the latter. By making a coming soon tag or an empty section, you are committing yourself to adding the content in the near future.

Googolists often plan some content, and never create it, because t…

• ## Stronger Bird's Array notation

July 30, 2017 by Bubby3

Did you know you can make ~ behave like ,, in SAN if you change a few rules.

Everything up to [1[1~3]2] remains unchanged.

Comparisons between mine and Bird's expression.

[1[1[1~3]2~2]2[1~3]2] in my system is equal to [1[1~3]3] in Bird's system.

[1[1[1~3]2~2]3[1~3]2] in my system is equal to [1[1~3]4] in Bird's system.

[1[1[1~3]2~2]1[1[1~3]2~2]2[1~3]2] in my system is equal to [1[1~3]1[1~3]2] in Bird's system.

[1[2[2~3]2~2]2[1~3]2] in my system is equal to [1[2~3]2] in Bird's system.

[1[1\2[1~3]2~2]2[1~3]2] in my system is equal to [1[1/2~3]2] in Bird's system.

[1[1[1[1~3]2~2]2[1~3]2~2]2[1~3]2] in my system is equal to [1[1[1~3]2~3]2] in Bird's system.

[1[1[1[1[1~3]2~2]2[1~3]2~2]2[1~3]2~2]2[1~3]2] in my system is equal to [1[1[1[1~3]2~3]2~3]2] in B…

• ## Bashicu matrix system analysis

July 18, 2017 by Bubby3

(0,0,0)(1,1,1) has level $$\psi(\Omega_\omega)$$

(0,0,0)(1,1,1)(1,1,0) has level $$\psi(\Omega_\omega+1)$$

(0,0,0)(1,1,1)(1,1,0)(2,1,0) has level $$\psi(\Omega_\omega+\Omega)$$

(0,0,0)(1,1,1)(1,1,0)(2,2,0) has level $$\psi(\Omega_\omega+\psi_1(0))$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1) has level $$\psi(\Omega_\omega+\psi_1(\Omega_\omega))$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0) has level $$\psi(\Omega_\omega+\psi_1(\Omega_\omega+1))$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,2,0) has level $$\psi(\Omega_\omega+\Omega_2)$$

(0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)(3,3,0)(4,3,0) has level $$\psi(\Omega_\omega+\Omega_3)$$

(0,0,0)(1,1,1)(1,1,1) has level $$\psi(\Omega_\omega*2)$$

(0,0,0)(1,1,1)(2,0,0) has level $$\psi(\Omega_\omega*\omega)$$

(0,0,0)(1,1,1)(2,1,0) …

• ## Psi function type I and II comparison.

July 16, 2017 by Bubby3

The function types diverge at $$\Omega_2$$

Here is the comparison.

Function A Function B
$$\psi(\psi_1(\Omega_2))$$ $$\psi(\Omega_2)$$
$$\psi(\psi_1(\Omega_2)+1)$$ $$\psi(\Omega_2+1)$$
$$\psi(\psi_1(\Omega_2)+\Omega)$$ $$\psi(\Omega_2+\Omega)$$
$$\psi(\psi_1(\Omega_2)*2)$$ $$\psi(\Omega_2+\psi_1(\Omega_2))$$
$$\psi(\psi_1(\Omega_2+1))$$ $$\psi(\Omega_2+\psi_1(\Omega_2+1))$$
$$\psi(\psi_1(\Omega_2+\Omega))$$ $$\psi(\Omega_2+\psi_1(\Omega_2+\Omega))$$
$$\psi(\psi_1(\Omega_2+\psi_1(\Omega_2)))$$ $$\psi(\Omega_2+\psi_1(\Omega_2+\psi_1(\Omega_2)))$$
$$\psi(\psi_1(\Omega_2*2))$$ $$\psi(\Omega_2*2)$$

So the function catches up at $$\Omega_2*2$$ and all multiples of $$\Omega_2$$.

I like Function B better because it is more extensible.