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# Some Amazing Properties of 1

Stay_Classy
Recently, I saw a video talking about a number "Wau," which appeared a bit like an F. If one were to carefully look at all the maths, one would realize that it is talking about 1, and some interesting properties of it.

These equations look ugly without MathML, so write them down correctly on paper if you want them to look right.

1^1^1^1^1^1^1 = 1.

If x/y = 1, then x = y, so x^y^x^y^x/y^x^y^x^y = 1.

If the area of a rectangle is 1, and the height is 1, then the width is also 1.

Can anyone else think of some interesting properties?
nayakjyotirmaya
zero is invented in india.
vedic mathematics of india holds the key to the universe.
mazito
the number 1 is very useful and a lot of students forgot some partialy and the get wrong, i always think in any number (dont write it just in my head) is multiply for 1 , divide by 1 and power to 1 but never write it, but there is.

an easy example is x/xx is equal to 1/x but i see some people made the mistke of 0/x

other to work with rationals 5 multiply by 2/3 if you think in the 5 as 5/1 is easy to use the theorem of multiply rationals (a/b)(c/d)=ac/bd

or use to multiply algebra whe the literal is the same.

those propoerties is spread in diferents postulates or theorems definitios, but is handy to get in one sentence
Arrogant
1^infinity is indeterminant...
But i forgot why?
_AVG_
Here is another interesting fact about 1:

e^(0) = e^(2*pi*i) = e^(4*pi*i) = e^(n*pi*i) = 1
asnani04
The beauty of mathematics gets ever so enchanting. Especially, when it comes to Number Theory. And undoubtedly, 1, being the Multiplicative Identity, is one of the cornerstones of this exceptional diversity and range of number theory. Unity is a symbol that one is so familiar with, maybe even more than zero, that it symbolizes mathematics at times.

Also, 1 is great in the sense that it turns out to the final answer of many objective type problems on algebra, involving multiplication or division.
Arrogant
Yeah its all 1's and 0's in computer too.. Well maybe that doesn't count
But 1 is true
_AVG_
Here's another interesting one:

sqrt(1+sqrt(1+sqrt(1+sqrt(1+..... = 1 + 1/(1+1/(1+1/(1+1/(1+.... = the golden ratio

it's nice how so many 1s can be arranged to obtain the golden ratio
twotrophy
 asnani04 wrote: The beauty of mathematics gets ever so enchanting. Especially, when it comes to Number Theory. And undoubtedly, 1, being the Multiplicative Identity, is one of the cornerstones of this exceptional diversity and range of number theory. Unity is a symbol that one is so familiar with, maybe even more than zero, that it symbolizes mathematics at times. Also, 1 is great in the sense that it turns out to the final answer of many objective type problems on algebra, involving multiplication or division.

When I first started learning complicated Algebra, I did not really enjoy it because it seems that it is not useful to me. However, it turns out to be useful when I started finding out about how interesting mathematics is. Unfortunately, I still find mathematics difficult.

Also on another topic, I would like to admit that I have seen this thread a long time ago but I did not want to reply because I do not have any ideas on how to reply to this thread.