I was thinking about using combanation or permutations

I wonder if it's on Pascal's triangle??

# The Numberphile Topic -- The Official Nerdy Math Topic! [OLD]

**JonnyGamer**#256

**BuildASnowman**#257

Every number is in pascal's triangle (second column is every natural number), but this number doesn't appear in the first thousand rows, and therefore it's position can't be described in less than 3 characters. (Also, computer checked, doesn't appear in the first few million rows either)

**t1_hopscotch**#258

I was just looking at that line in your profile bio again @JonnyGamer on:

(I remember wondering and thinking I'd never really understand it. But then I found the Khan Academy video, and it explains it wonderfully; it was the first time I could come to understanding it I love Khan Academy)

I also think of this other comic from Murderous Maths :

And yeah I was looping through all the operations in my mind that I knew (though not as many hehe ) but couldn't think of anything either! @XiaoMiaoMi's initial thought of `10! = 3,628,800`

seemed soo close to `3,628,200`

though.

**t1_hopscotch**#259

And wow I hadn't heard of tetration before you both mentioned, but I think it is cool how:

- tetration = iterated exponentiation
- exponentiation = iterated multiplication
- multiplication = iterated addition
- (addition = repeated +1s)

Is there more??

It is funny because I remember when there was no multiplication operator in Hopscotch, there was a calculator replicating it by using Repeat and Increase Value.

Then when there was no exponent operator in Hopscotch, I replicated it by using Repeats and multiplication.

And now... nah kidding

Okay I was tempted, this was fun to think about...

(Note!! I don't know if this will work or anything, just thinking about it here)

```
Add(m, n):
Set result to m
Repeat times n
Increase result by 1
End
Multiply(m, n):
Set result to 0
Repeat times n
Set result to result + m
End
Exponent(m, n):
Set result to 1
Repeat times n
Set result to result * m
End
Tetration(m, n):
Set result to m
Repeat times n
Set result to m ^ result
```

Tell me if I misunderstood anything

**BuildASnowman**#260

Yup! It goes farther. In fact, it goes *infinitely* farther with something called Knuth's Up Arrow Notation. It's kind of hard to wrap your head around, but one up arrow is regular exponentiation:

4 ↑ 3 = 4^{3}

Then 2 arrows is tetration:

4 ↑ ↑ 3 = 4^4^4

Then 3 arrows is the hyperoperation above that (pentation, iterated tetration):

4 ↑ ↑ ↑ 3 = 4 ↑ ↑(4 ↑ ↑4)

And so on. It can be extended infinitely. It's super cool.

**JonnyGamer**#264

Build a Snowman, thanks for explaining it! I found an article about this that take some you to extreme numbers like Graham's Number. Graham's is vastly ginormous and takes the Knuth's Up Arroe Notation to the extreme

Graham's Number Link _{ There happens to be a little profanity in this one..}

There's also a Numberphile video!

Graham's Number Video

I really enjoy this stuff! Creating extremely large numbers is called googology, and there's actually an entire wiki for that! Googology Wiki

And if you like that, a person named Sbiis Saibian made an entire web book on it Googology Web Book.

**Kiwicute2013**#265

Fortunately, your question is not asking to simplify the number in three characters, but simply asking if it **can** be simplified in three characters, and because I am always right unless you prove me wrong,

the answer is: *no. It can not be simplified in three characters cause i said so.*

**JonnyGamer**#266

Hello! You haven't been back in a while!

I think @DECODO was mistaken with 10!

(Thanks to @XiaoMiaoMi for that)

**t1_hopscotch**#270

Ooh woah thanks for that @JonnyGamer and BAS! So was this what you were talking about when you mentioned hyper operations JonnyGamer? Pentation = iterated tetration, hexation = iterated pentation etc wow

googology sounds like it must have originated from googol, in which case it sounds like an appropriate name. And I can see you are very excited about this!!

Wow I just looked at that first link – thanks for the warning, I skimmed past it mostly – and it got climatic very quickly (Though it made me think of a post I'd read on our scope insensitivity to large numbers which I was conscious of hehe)

**t1_hopscotch**#271

I just saw @Fishyguitars post this and I am just in the middle of watching and (although I have in fact seen this in a book already — yup one of the Murderous Maths books but it was a long while ago) it sounds very interesting so far!

TED-Ed is great, I might include it in the Want More Math topic too.

**JonnyGamer**#272

Yes! I am very excited!

I've been into large number since I was in Kindergarten

(Funny story, actually, I write the numbers 1 - 6000 in a tiny notebook in Kindergarten )

**MR.GAM3R**#273

I was wondering about this today and wanted to know what you guys think.

In words, what is this number? `-12`

Is it "minus twelve" or "negative twelve"? Is there a right or wrong? What do *you* call it?

**t1_hopscotch**#274

That is interesting to think about I have heard it called both, but I think I say negative twelve when talking. I guess minus twelve could also mean like subtracting twelve (and maybe a bit more risk of confusion but I don't usually see that happening haha, just hypothetical )

**JonnyGamer**#275

I think minus twelve is a slang for 0 - 12, which is negative twelve. I use negative, since it can cause confusion with the subtraction operator.

Like (-5) - (-7)

Is minus five minus minus seven.

That makes less sense than..

Negative 5, minus Negative 7