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Some weird math I thought of

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WalkerInTheWoods

quote:
0^0 * 1^1 * 2^2 * 3^3 * 4^4 * 5^5


Isn't 0 * any number = 0?
Better take the 0 out of the equation. [;)]
Alice had got so much into the way of expecting nothing but out-of-the-way things to happen, that it seemed quite dull and stupid for life to go on in the common way.

Aries

Im not sure about what your meaning but I heard that 43 was a special number.
I heard that everytime you see the #43 there is a life changing event that can happen, provided you choose the right path of course.
And strange things have happened to me, one time I was coming back from a trip, I was getting off the plane at an airport, and standing next to the entrance into the airport from the plane was a guy wearing a shirt that had the number 43 on the front. As soon as I got into the airport he turned around and walked off.
What was he just standing there for?? Why did he happen to walk away right after I noticed the 43 on his shirt??
Hmmm anyone else notice the #43 alot or had anything bad happen after seeing it?
-Aries
How can the spoon know the taste of soup?

WalkerInTheWoods

Sorry, my bad. I forgot 0^0 = 1.
Alice had got so much into the way of expecting nothing but out-of-the-way things to happen, that it seemed quite dull and stupid for life to go on in the common way.

lifebreath

Or the number of milliseconds in one day...

That, btw, is the sequence of hyperfactorials ...

The next in the sequence is 4,031,078,400,000, which equals the number of seconds in 46,656,000 days and 46,656,000 = 360^3 = (72*5)^3 so it's related to phi via the pentagram and 4,031,078,400,000 is divisable by 111 ... Lot's of interesting numbers in there ...

Jeff_Mash

Keep smiling,

Jeff Mash
http://www.mjmmagic.com

WalkerInTheWoods

I figured out what beavis is talking about and then life has to go and throw all that out. Ouchie lol

I do not understand how nothing * nothing = 1. 1 nothing is still nothing. lol
Alice had got so much into the way of expecting nothing but out-of-the-way things to happen, that it seemed quite dull and stupid for life to go on in the common way.

lifebreath

and BTW, 0^0 is *undefined*, not 1. n^0 = 1, for all n not equal to 0.

WalkerInTheWoods

quote:
and BTW, 0^0 is *undefined*, not 1.


Then why does my calculator say it is 1?
lol I have not done this some of this in awhile.
Alice had got so much into the way of expecting nothing but out-of-the-way things to happen, that it seemed quite dull and stupid for life to go on in the common way.

beavis

0^0 = 1

because there are no zeros multiplied (exponent of 0)

so it = 1 for the same reason (everything else)^0 = 1, that none of that number is multiplied.

lifebreath

quote:
0^0 = 1

because there are no zeros multiplied (exponent of 0)

so it = 1 for the same reason (everything else)^0 = 1, that none of that number is multiplied.


Not really. The generalized power function f(x,y) = x^y is discontinuous and undefined at x = y = 0, which is the context of your original usage.

0^0 is *defined* as equal to 1 as a *convention* of convenience in other areas. For a discusion this convention:

http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

http://www.math.hmc.edu/funfacts/ffiles/10005.3-5.shtml?CFID=1146928&CFTOKEN=41937423&jsessionid=06303118541071203517908

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

So, it's a bit of hair splitting, but your original observation is a good one, and still holds without the 0^0 expression.

Try this link for lot's of interesting numbers:

http://home.earthlink.net/~mrob/pub/math/numbers.html

beavis

Anything with an exponent of 0 is undefined because it contains zero numbers. Because it contains zero numbers, it can be multiplied by anything and it wont change the original number.

0^0 * a = a

Thats why we define it as 1. But defined or not, my equation is still defined with 0^0, by the strictest of rules.

beavis

The number of seconds in 1000 days
= 1000 * 24 * 60 * 60
= 0^0 * 1^1 * 2^2 * 3^3 * 4^4 * 5^5

I thought of this after being told that 108 is the Buddhist "magic number" or something like that. Then I found its factors which are 2, 2, 3, 3, 3, and that equals 0^0 * 1^1 * 2^2 * 3^3. So I found the later numbers in the set and noticed it was the number of seconds in 1000 days.