More large numbers?

by googology101, Mar 18, 2009, 7:04 PM

Wow! It's been quite a while since I've updated this...

Anyways...

$pigol = \underbrace{3141\ldots}_{100}$

$egol = \underbrace{2718\ldots}_{100}$

$phigol = \underbrace{1618\ldots}_{100}$

Yeah, this blog is back, and it's even worse than ever.

Meg[i][a]st[r]on

by googology101, Feb 27, 2009, 5:37 PM

I'm totally stuck. Read this:

http://mathworld.wolfram.com/Megistron.html

And this:

http://www.mrob.com/pub/math/largenum-4.html

And this:

http://www.polytope.net/hedrondude/scrapers.htm

So, is this crazy number named Megistron, Megiston, or Megaston? Does anyone really care?

Again, numbers

by googology101, Feb 19, 2009, 6:36 PM

$gaoogol =\ ^{10^{100}}10$
$gaooaggol =\ ^{10^{^{100}10}}10$
$gooaggol = 10^{^{100}10}$
$gooaoogol = 10^{^{10^{100}}10}$
$gaooaooaggol =\ ^{10^{^{10^{^{100}10}}10}}10$

It's hard to get these numbers by looking at the $\text{\LaTeX}$ . Look at the code, it might help.

Numbers

by googology101, Feb 19, 2009, 12:38 AM

$gooiol = 10^i$
$gooiolplex = 10^{10^i}$

You get it.

Using strange and pointless combinations of tetration and exponents, we have

$googol = 10^{100}$
$googolplex = 10^{10^{100}}$
$gaggol = ^{100}10$
$gaggolplex = ^{^{100}10}10$

Okay, I didn't make up those four.

$gooaggol = 10^{^{100}10}$
$gooaggolplex = 10^{^{goaggol}10}$
$gooaggol = 10^{^{100}10}$
$gooaggolplex = 10^{^{goaggol}10}$

Visualizing a googol

by googology101, Feb 17, 2009, 4:10 AM

Okay. HEEEEERE we go. Here's how we imagine a googol dots.

First, imagine a dot.

Now, imagine ten of those in a line.

Now think of a square made of ten lines above.

Think of that square made ten times into a cube.

Now think of that cube. Mentally pack that cube into one dot. Now perform the process above on that one dot and unpack.

Pack again, multiply, and unpack.

Pack again, multiply, and unpack.

Pack again, multiply, and unpack.

Say that 31 times.

Now pack that cube up again. Line up ten of these dots as in step 2.

Unpack. That's a googol. Tiny, isn't it?

Go to sleep, if you haven't already.

Blah

by googology101, Feb 13, 2009, 3:04 AM

$ blahgol = \left(\sum^{10^{100}}_{i = 0} \sqrt {i}\right\) - \left(\sum^{10^{100}}_{i = 0} \mathrm{frac}\left(\sqrt {i}\right)\right)$

$blahgolplex = \left(\sum^{blahgol}_{i = 0} \sqrt {i}\right) - \left(\sum^{blahgol}_{i = 0} \mathrm{frac}\left(\sqrt {i}\right)\right)$

$yadayadayadagol = \left(\sum^{10^{100}}_{i = 0} \sqrt [3]{i}\right) - \left(\sum^{10^{100}}_{i = 0} \mathrm{frac}\left(\sqrt [3]{i}\right)\right)$

$yadayadayadagolplex = \left(\sum^{yadayadayadagol}_{i = 0} \sqrt [3]{i}\right) - \left(\sum^{yadayadayadagol}_{i = 0} \mathrm{frac}\left(\sqrt [3]{i}\right)\right)$

We could go on with yakkety-yakgol, using $\sqrt [4]{i}$ .

Bored?

Hypermathematics

by googology101, Feb 12, 2009, 1:00 AM

Okay, I've got some things cleared up. If you've studied up on your googology, then you'll know the basic hyper-operators: addition, multiplication, exponentation, tetration, pentation, hexation (or sextation if you don't like the Greek pattern) and so forth.

So, now to twist the rules.

I've invented a hypothetical type of mathematics called hypermathematics. Hypermathematics is unusual because of its difference in the hyper-operators. The difference? It doesn't start with addition, it starts with concatenation. So, in not-so-hyper-land,

$2 + 2 = 22$

Yes, it seems stupid. But that's how they go. This gives us multiplication, where $3 \cdot 3 = 3 + 3 + 3 = 333$ , exponentation, where $2^{3} = 2 \cdot 2 \cdot 2 = 22 \cdot 2 = 22 + 22 = 2222$ , and tetration, where $^33 = 3 \cdot 3 \cdot 3 = 333 \cdot 3 = 333333333$ .

(The main pitfall is that there is no true definition for the counting numbers. Since $3 + 1 = 31$ , there is no way we can define 4, unless we convert back to standard math.)

Now for the boring part. Using hypermathematics,

$coogol = hyper(10,3,100)$

$coogolplex = hyper(10,3,hyper(10,3,100))$

You get the point. We've got ciggol, caggol, ceegol, cigol, coggol, cagol, cboogol, congol, and all the plexes. And I've finally got you to sleep.

More random numbers

by googology101, Feb 11, 2009, 5:42 PM

$ggoogol = centagoogol$

$biggoogol = \left\langle ggoogol, ggoogol \right\rangle$

$triggoogol = \left\langle ggoogol, ggoogol, ggoogol \right\rangle$

I promised no more migraine jokes.

$gggoogol = centaggoogol$

I'm staying quiet...

$gwgoogol = \underbrace{ggg\ldots ggg}_{100}oogol$

Random numbers

by googology101, Feb 11, 2009, 2:35 AM

$bigoogol = \left\langle 10^{100}, 10^{100} \right\rangle$ (those funky angle brackets mean concatenation)

$trigoogol = \left\langle 10^{100}, 10^{100}, 10^{100} \right\rangle$

$quadrigoogol = \left\langle 10^{100}, 10^{100}, 10^{100}, 10^{100} \right\rangle$

Continue to sleep.

A revolution!

by googology101, Feb 10, 2009, 1:32 AM

Yay! I'm the 2000th visitor!

Submit

11 year bump
by john0512, Dec 28, 2020, 3:03 AM
Sure.
by googology101, Feb 12, 2009, 12:38 AM
me want contrib
by gauss1181, Feb 11, 2009, 5:49 PM
Sorry, I ran out of time on the last shout...
by googology101, Feb 8, 2009, 11:19 PM
and contrib?
by james4l, Feb 8, 2009, 4:42 AM
I guess...
by googology101, Feb 7, 2009, 11:49 PM
contrib please
by james4l, Feb 7, 2009, 10:18 PM
Yeah, I noticed that too. I'll change it later, but there's a weird glitch for you. The top and left properties should be automatically set to 0 if position is set to absolute or fixed. Go Firefox!
by googology101, Jan 21, 2009, 10:03 PM
i viewed this from ie and it looks like position fixed also ruins the left aligned so put left:0. nice submit buttons
by Sephiroth, Jan 21, 2009, 5:32 AM
Use filter:alpha(opacity=80) to make it semitransparent in IE. And make sure you use -moz-opacity instead of opacity to make sure that older versions of Firefox will cooperate. And by the way, you're free to copy the code. The whole thing is at http://www.artofproblemsolving.com/Forum/templates/blogs/Hyperion/style/c1366.css
by googology101, Jan 19, 2009, 9:50 PM
add filter: alpha(opacity=80) and opacity:0.8
by Sephiroth, Jan 19, 2009, 3:51 AM
Could I use that code in my blog?
by dysfunctionalequations, Jan 19, 2009, 1:51 AM
Watch out! position:fixed ruins the box's 100% width. Here's the code I used:

#navigation_box {
background-color: #005500 !important;
border-bottom-style:solid !important;
-moz-opacity:0.80;
color:white !important;
position:fixed !important;
width:100%;
padding-right:10px;
}

Don't overdo the opacity. 0.80 or 0.90 will do. Sorry, IE and Safari users, you aren't seeing it.
by googology101, Jan 19, 2009, 1:26 AM
what do you mean by floating menus? like how he made navigation_box fixed? he used "#navigation_box{ position: fixed;}" i like how you made it opacity
by Sephiroth, Jan 18, 2009, 4:45 AM
Floating menus? How do you do that?
by dysfunctionalequations, Jan 18, 2009, 1:25 AM
Yup. I'm trying to post daily.
by googology101, Jan 14, 2009, 12:05 AM
3rd post!
by 007math, Jan 13, 2009, 11:57 PM
Do you mean to this blog?
by googology101, Jan 12, 2009, 9:30 PM
Can i be a contributor?
by Wickedestjr, Jan 12, 2009, 5:49 PM

19 shouts

A googol is a tiny dot