Singapore Expats

While just analysing, I found that we are on base 9 for atleast the first set of 10 Nos and have inadvertently given a value of 1 , to zero.

For instance, in Base 2 = it goes 0,1,10,11,100..
we see that , 10 happens only in the 3rd place, which is (Base 2+1)

Hexadecimal too is right, as alphabets A-F have been allocated to represent 10-15... So including the 0, we get 16 numbers and we get 10 to represent 16, only in the 17th place.

But in decimal alone, we see that 10 is already a 2 digit number, making ours a Base 9 System as inadvertently 9 has been doing the job of 10 in the decimal system we have been following.

Has anyone come across this or is it that I am missing some thing?

for easy reference you may visit this page,
http://en.wikipedia.org/wiki/Binary_numeral_system

One can also find the anamoly, if we rework from Hex to decimal.

I'll have some of what you are smoking.

0 1 2 3 4 5 6 7 8 9

Count 'em. TEN symbols

0 1

TWO symbols

Quite True, as we often fall for this.

But you can see 10 occupying the place below 2. With 0 included 2 does not appear in Base 2. Logical.

But Just go on in the sequence, you will see 10 appearing for Base 9. And logically 10 can't appear in a Base 10 and should occupy 11. Use a roman X, which is single character & work for Base x.

Strong Eagle wrote:I'll have some of what you are smoking.

0 1 2 3 4 5 6 7 8 9

Count 'em. TEN symbols

0 1 # # # # # # #

TWO symbols

I don;t even think I want any of what he's smoking.

You miss the whole point.

a) There are two symbols in the binary system, 0 and 1. There is no 2 and 1 plus 1 = 10 because you carry.

b) There are ten symbols in the decimal system, 0 thru 9. There is no 10 and 9 + 1 = 10 because you carry.

In binary, each column, starting from the right represents 2 raised to the n'th power, as in (** = exponentiation, raised to a power).

2 ** 0
2 ** 1
2 ** 2, etc.

So, 10 = 2 ** 0 * 0 + 2 ** 1 * 1 = 2

For decimal it is

10 ** 0
10 ** 1
10 ** 2, etc.

So, 5 = 10 ** 0 * 5
14 = 10 ** 0 * 4 + 10 ** 1 * 1

You are way off base in your understanding. The 10 to which you refer in the decimal system only shows that there are 0 units an 1 10 units.

Thanks for taking pains & I know it can be a bit taxing to review elementary work. But the bug is also a moving phenomenon, for it makes what we look into as right, but pushes the bug to other side.

I have worked this for your easy reference.
You agree that there are 2 symbols in binary , so it is base 2. instead of 0,1 try 1,2 & so on.. effectively I am throwing the 0 out.

Base 1 1X
Base 2 12X
Base 3 123X
Base 4 1234X
Base 5 12345X
Base 6 123456X
Base 7 1234567X
Base 8 12345678X
Base 9 123456789X
Base 10 123456789AX
Base 11 123456789ABX
Base 12 123456789ABCX
Base 13 123456789ABCDX
Base 14 123456789ABCDEX
Base 15 123456789ABCDEFX
Base 16 123456789ABCDEFGX

So in every case above we see X after the base value. But in Base-10 we see that A is required, but not in practise.

When 0 is included, Base 10 would be right, but Base 1, will have no value, Since there is nothing to carry. So base 10 shifts to base 1 for single digit, with 0 included.

Reason why I say we have been following a Base 9, thinking we are in decimal, since in our practise we don't use 0. When we count fingers, we count from 1 to 10. (we don't include 0.) and so we have 10 fingers.

With 0 not included 1-9, is only 9 elements and +1 we carry to make 10 fingers and that we use Base 9 , is my contention.

Shankar wrote:Reason why I say we have been following a Base 9, thinking we are in decimal, since in our practise we don't use 0. When we count fingers, we count from 1 to 10. (we don't include 0.) and so we have 10 fingers.

If I ball my hands into fists and ask you to tell me how many fingers I'm holding up, what will you answer?

jpatokal wrote:

Shankar wrote:Reason why I say we have been following a Base 9, thinking we are in decimal, since in our practise we don't use 0. When we count fingers, we count from 1 to 10. (we don't include 0.) and so we have 10 fingers.

If I ball my hands into fists and ask you to tell me how many fingers I'm holding up, what will you answer?

you would be holding up Zero, if the first time.
and X , if it's the second time (where x= no. of fingers in no. of hands)

Shankar wrote: Base 1 1X
Base 2 12X
Base 3 123X
Base 4 1234X
Base 5 12345X
Base 6 123456X
Base 7 1234567X
Base 8 12345678X
Base 9 123456789X
Base 10 123456789AX
Base 11 123456789ABX
Base 12 123456789ABCX
Base 13 123456789ABCDX
Base 14 123456789ABCDEX
Base 15 123456789ABCDEFX
Base 16 123456789ABCDEFGX

But in Base-10 we see that A is required, but not in practise.

Your same silly thinking holds for all the examples you gave above.

Base 2 - 2 is required but not in practice.
Base 16 - G is required but not in practice.

Is there a point to all this nonsense? You really ought to do some reading on the history of arithmetic. The invention of 0 is what made real arithmetic and mathematics possible. And yes, there are TEN symbols in base 10

0 1 2 3 4 5 6 7 8 9

Hello? Hello? I don't think you've reached Nirvana yet.

PS: Base 1 can never be used for counting because 1 raised to any power is still 1.

So am I right to say this is a Base 2 or binary discussion because only two posters - Shankar and SE - even vaguely know what this thread is all about?

0 - Shankar
1 - SE

Wind In My Hair wrote:So am I right to say this is a Base 2 or binary discussion because only two posters - Shankar and SE - even vaguely know what this thread is all about?

0 - Shankar
1 - SE

ooops... forgot to backup.

Shankar wrote: Base 1 1X
.

Smoke aside, does Base 1 even exist?

Spunky wrote:

Shankar wrote: Base 1 1X
.

Smoke aside, does Base 1 even exist?

I see you have a wooden spoon!