Base 10 Number System Question

[boc4life]

I'm trying to understand some concepts behind the Base 10 number system, and I have a few questions.

Imagining a scenario where after the number 9 came the "number" A

1. What would the order of numbers be?
...8, 9, A, 10, 11, 12...18, 19, 1A, 20, 21...

Does that look right?

2. Would this number system be described as a "Base A" system?

3. (Unrelated to the imaginary number system) Why is Binary referred to as a Base 2 system, when the number 2 does not even exist within the system?



Do I appear to be way off in my thinking?

[SBR]

1) Yes

2) No it would be called base 11

3) Base X refers to a number system with X digits. So a binary or base 2 system has 2 digits (0,1) and the "regular" number system is base 10 (0,1,2,3,4,5,6,7,8,9)

[boc4life]

[ QUOTE ]
1) Yes

2) No it would be called base 11

3) Base X refers to a number system with X digits. So a binary or base 2 system has 2 digits (0,1) and the "regular" number system is base 10 (0,1,2,3,4,5,6,7,8,9)

[/ QUOTE ]

What confuses me is that for our number system, referred to as Base 10, the number 10 exists on the number line. If the only number system in the world that existed was the Binary system, and the numbers 2-9 did not exist, what would we refer to the system as? Consider the same question for my fictional "A" system.

[vhawk01]

The number ten doesnt really exist though. Its simply a 1 in the tens place and a 0 in the ones place. But I suppose I see where you are going, in that we had the benefit of a developed numbering system before we formally structured it and considered other base systems.

[SBR]

[ QUOTE ]
[ QUOTE ]
1) Yes

2) No it would be called base 11

3) Base X refers to a number system with X digits. So a binary or base 2 system has 2 digits (0,1) and the "regular" number system is base 10 (0,1,2,3,4,5,6,7,8,9)

[/ QUOTE ]

What confuses me is that for our number system, referred to as Base 10, the number 10 exists on the number line. If the only number system in the world that existed was the Binary system, and the numbers 2-9 did not exist, what would we refer to the system as? Consider the same question for my fictional "A" system.

[/ QUOTE ]

You need to put a little more thought into this. The number 2 exists in binary as well its just represented as 10. If a base 2 number system was common then we could give the number 10 a special name.

The number ten doesn't exist any more or less than the number (binary) 10. We just give it a special name.

[FortunaMaximus]

Look at your hands. Primal logic. Ten of 'em, right?

The definition of a base is how many distinct digits it contains.

Base 2 (binary) 0, 1. Two digits
Base 10, standard counting system, 0-9 has 10 digits
Base 16, commonly known as hexadecimal, used in computing.
(0-9, A-F)

Putting "A" in the middle of a base would only expand it, in this case, to Base 11, 0-8, A, 9.

Hope that's helpful. Cheers.

[RocketManJames]

Yes, you're pretty much right that it would be called a Base A system in a world that was based upon a Base 11 system (that is... Base 11 in our Base 10 world).

Base 10 in a world that adopted the Base A system would be Base 12 in our world.

Is this what you're getting at?

-RMJ

[boc4life]

[ QUOTE ]
Yes, you're pretty much right that it would be called a Base A system in a world that was based upon a Base 11 system (that is... Base 11 in our Base 10 world).

Base 10 in a world that adopted the Base A system would be Base 12 in our world.

Is this what you're getting at?

-RMJ

[/ QUOTE ]

I believe this is what I'm getting at. As someone said earlier in the thread, the number 2 DOES exist in binary, it's just represented as 10.

Does this mean that for someone who spoke and thought in binary, their system would also be referred to as a "Base 10", with 10 representing a completely different number than the 10 that we know?


Also, referencing another previous post...Is it likely that the Base 10 system that we use was developed because humans have 10 fingers?

[FortunaMaximus]

It's not only likely, it's the simplest possible explanation. And I can't find a better or even worse one.

[disjunction]

It looks your original question has been answered so I'll throw a couple of more thoughts out there. It sounds like you may not be familiar with this, but all computer people think in Base-16. It is very useful to know. Wife permitting, I am personally going to teach my kids to think in Base-16 or Base-32 and learn the appropriate multiplication tables. This will undoubtedly make them more adept at arithmetic.

The bottleneck in doing arithmetic in your head is memory, and with Base-16, there's simply less to remember. Four-digit numbers are now 3-digit numbers.

http://en.wikipedia.org/wiki/Hexadecimal