View Full Version : All is one in base 1

03-23-2015, 03:58 AM
A thought just came to me that in base 1, 1 represents infinity...I will pinch a bit from another post here to save rewriting it...

We can represent numbers in what is known as Bases, for instance we normally count in
decimal, which is base 10.

What is base 10?

Base 10 is a way to classify a “column” of numbers and in each column we can have one less
than the base number, so in base 10 (decimal) we can have up to nine in any one column and
if we exceed that then we have to put one into the next column and that represents an order
increment. The columns go up in order of the base number and in decimal this is 10 so the
columns looks like:

10,000 │ 1,000 │ 100 │10 │ 1 (or units)

Sounds confusing, but all it is saying is that we can have 1, 2, 3, 4, 5, 6, 7, 8 or 9 all under
one column, but if we add one more after we reach 9 the we put 1 into the next column and
start at zero again in the first column and we represent that as 10…one ten and no units. This
is the same for all the columns.

Columns are calculated by powers of the base, so column one in any base number is the
base number to the power of zero; if you didn’t already know, any number to the power of
zero is “one”; if you have a calculator that can do powers then put in the numbers and see
for yourself.

The next column is the base to the power of one. Any number to the power of one is the
number itself, i.e. it doesn’t change; again try it yourself; so ten to the power of one is just ten
and this will always be in the second column so if we know our BASE we know the second
column is representing whatever number is in it multiplied by the BASE…in the case of
decimal (base 10) 10 represents 1 x 10 = 10. To represent twenty we put 2 in the second
column and we get 2 x 10 = 20

Thus if we have 3 lots of 100’s, 5 lots of 10’s and 4 lots of 1’s we just write it as 354 and take
it for granted that this is what we have, three hundred and fifty four, so the number 354 in columns
looks like:


Now if we were to count in base 6, then each column could only have 1, 2, 3, 4, or 5, for if
we added one more after 5 we would put 1 into the next column and start at zero again in the
first column and we represent that as 10…one six and no units. Again the columns go up in
orders of the base. We can still have the number 354, but this is not the same value as we
had in base 10, for now we have 3 lots of 36’s, 5 lots of 6’s and 4 lots of 1’s; if we add this up
then we can see that 354 in base 6 only represents 142 in base 10.


This doesn’t mean we can’t represent decimal 354 in base 6 it just means it is going to look
a little different as below:


Therefore 1350 (Base 6) = 354 (base 10)

I hope that wasn’t too confusing because we are now going to apply the exact same
principle to base 2 (BINARY). In base 2 (binary) the highest number we can have in one
column is 1, for if we add another 1 to it we have to put 1 into the next column and start
column one at zero. I won’t write the explanation just look at the picture and see if you can
understand what is happening.


Therefore 101100010 (Base 2) = 354 (base 10)

Note: 1 in column 2 is 1 x 2 = 2 which is the BASE...get it? base 2.

The point I am trying to make is that if we see "10" then we say ten, but that is only true
in decimal; "10" in base 2 is two, "10" in base 7 is seven. We miss the true representation and that
is why we find working in anything other than decimal complex, when it isn't at all if you look
at it correctly.

Now you have a full understanding of bases let's look at Base 1. There is not a true representation of Base 1 as there would be no way to represent any number other than 1, so a totally different notation exists where they throw everything written above out of the window and this is called The Unary numeral system (http://en.wikipedia.org/wiki/Unary_numeral_system)

I won't go into that here, but rather stick to the notation above.

Using this notation you may remember that you can only represent one less than the base number in any column. In this case the base is 1, and so we must move the 1 to the next column and put a zero in the column before, BUT in the next column it still exceeds the allowed column number and thus we need to move to the next column and put a zero in the one before and this continues ad infinitum.

http://thealchemyforum.com/Images/RAM/BASE 1.png

You can check this out on your calculator where 1 to any power still equals 1.

1 x 1 x 1 x 1=1

Possible Conclusion

A possible conclusion may be that this shows that the true representation of one is infinite; one is all and all is one; everything else is just an illusion of convenience. You can't pin the one down, for as soon as you think you have, it has moved on.

I hope I explained that clearly :)