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Looks like we are following Base-9 thinking we are decimal.

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Shankar
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Looks like we are following Base-9 thinking we are decimal.

Postby Shankar » Mon, 22 Oct 2007 6:57 pm

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.
recently attained my Nirvaana and became a Budha.

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Postby Strong Eagle » Tue, 23 Oct 2007 8:16 am

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

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Shankar
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Postby Shankar » Tue, 23 Oct 2007 8:42 am

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
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Allibert
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WTf?

Postby Allibert » Tue, 23 Oct 2007 10:46 am

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

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Strong Eagle
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Postby Strong Eagle » Tue, 23 Oct 2007 2:22 pm

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.

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Shankar
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Postby Shankar » Tue, 23 Oct 2007 5:38 pm

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.
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Postby Plavt » Tue, 23 Oct 2007 6:12 pm

Image :lol:

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Postby jpatokal » Tue, 23 Oct 2007 11:34 pm

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? :P
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Shankar
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Postby Shankar » Wed, 24 Oct 2007 12:35 am

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? :P


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)
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Postby Strong Eagle » Wed, 24 Oct 2007 2:38 pm

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.

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Postby Wind In My Hair » Wed, 24 Oct 2007 3:02 pm

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? :P

0 - Shankar
1 - SE

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Postby mayamomi » Wed, 24 Oct 2007 3:15 pm

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? :P

0 - Shankar
1 - SE



:lol:
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To me, he's everything...

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Shankar
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Postby Shankar » Sat, 08 Dec 2007 10:46 pm

ooops... forgot to backup.
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Postby Spunky » Mon, 10 Dec 2007 11:15 am

Shankar wrote:Base 1 1X
.


Smoke aside, does Base 1 even exist?

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Postby ksl » Mon, 10 Dec 2007 2:49 pm

Spunky wrote:
Shankar wrote:Base 1 1X
.


Smoke aside, does Base 1 even exist?


I see you have a wooden spoon! :lol:


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