Calculating 2+2: The Answer Revealed

[gabe]

what is 2+2?

 

[ceptimus]

Lots of possible answers:

Using the + symbol as a Logical OR, the answer is 2

In base 3 the answer is 11

In base 4 the answer is 10

In every other possible base, the 'normal' answer is 4

I'm sure there are many other possibilities...

 

[TenaliRaman]

G = {Z,+,*}
2 e Z
2+2 e Z
:p

 

[The Bob]

Lots of possible answers:

Using the + symbol as a Logical OR, the answer is 2

In base 3 the answer is 11

In base 4 the answer is 10

In every other possible base, the 'normal' answer is 4

I'm sure there are many other possibilities...

Base?

The Bob (2004 ©)

 

[The Bob]

I am going to say 2+2 is 2+2 as the question does not say 'what is the answer to 2+2?' or 'what does 2+2 equal?'

My Answer: 2+2

The Bob (2004 ©)

 

[Ian Rumsey]

The ? may indicate another digit, so it could read 2+21 or 2+22 etc, etc

 

[gabe]

man your stupid, 2+2=4 even a 5 year old would know that

 

[K.J.Healey]

then its not really an expert puzzle now is it?

 

[Gokul43201]

man your stupid, 2+2=4 even a 5 year old would know that

And you must be about 7 years old, because even an eight-year-old will know that the correct word to be used in your punctuation challenged "sentence" - the only puctuation used is the wrong one and you really should have three sentences there - is "you're", not "your" !

<Just a note that I'm aware of the 'conjunction rule' which is really archaic - in case you were planning on bringing that up.>

 

[vsage]

Good one, Goku. You say what I think.

 

[The Bob]

So what was the point in posting it gabe if you didn't want an unusual answer?

The Bob (2004 ©)

 

[Jin314159]

man your stupid, 2+2=4 even a 5 year old would know that

lol... trollism at its finest.

 

[gabe]

it was a joke! man that was funny

 

[ceptimus]

Base?

The Bob (2004 ©)

All your base are belong to us.

 

[The Bob]

All your base are belong to us.

Not getting it at all.

In Confusion
The Bob (2004 ©)

 

[TenaliRaman]

123 can be written as,
1*10^2 + 2*10 + 3
This representation as we know it is called the decimal representation.
Also this is called the *base 10* representation
cuz the number is written in the powers of 10.
In general a base 10 number can be written as,
a_n*10^n + ...+a_1*10+a_0
where 0<= a_i <=9 for all 0<=i<=n

As we can have base 10 representaion then we can have any base 'r' representation ...
A base r number can be represented as,
a_n*r^n + ...+a_1*r+a_0
where 0<= a_i <=r-1 for all 0<=i<=n

e.g "5 in base 10" is "101 in base 2"
note that : 1*2^2 + 0*2 + 1 = 5

Hope this helps.
-- AI

 

[The Bob]

e.g "5 in base 10" is "101 in base 2"
note that : 1*2^2 + 0*2 + 1 = 5

I think it will help and has but could you please write out the bases, above, and their equations, like at the top of your post.

So 5 in base 10 = 5
101 in base 2 = 5 because 1*2^1 + 0 + 1?

Sorry I am a pain but I have little understanding of this.

Thanks

The Bob (2004 ©)

 

[ceptimus]

In base 10 we have 10 different symbols: 0,1,2,3,4,5,6,7,8,9

In (say) base 4, we only have four symbols: 0,1,2,3

so counting in base 4 looks like this: 0,1,2,3,10,11,12,13,20,21,22,23,30...

The 'ultimate' low base is base 2 where only two symbols are used: 0,1

This base is used by computers as the 0 and 1 can be easily represented by the absence or presence of a voltage, or current, or charge etc. Because it is so widely used, Base 2 has a special name: Binary.

Counting in Base 2 (aka Binary) looks like this: 0,1,10,11,100,101,110,111,1000...

Hope that helps.

'All of your base are belong to us' is a cult-saying on the internet. It came from a video game. Try googling on it to find more, if you're interested.

 

[The Bob]

I GET IT. Man, I am slow.

Sorry guys, I took ages to get that.

Thanks TenaliRaman and Ceptimus. Appreciate the help.

The Bob (2004 ©)

 

[check]

In base 1 how would zero be expressed? Would one count like:
0,00,000,0000 etc
or no zero and do 1,11,111,1111 ?

 

[The Bob]

The 'ultimate' low base is base 2 where only two symbols are used: 0,1

In base 1

No base 1. Don't know why but not base 1.

The Bob (2004 ©)

 

[nucleartear]

May be the fingers are an excellent example of base 1!

 

[TenaliRaman]

base 2 is the "ultimate" limit only if one considers the schema/representation i proposed.

ppl have come up with many different representations which is in close analogy with this base representation

If u consider 0,1,2,3,4,5,6,... as just weighted symbols and that any base r representation as a representation which uses no more than abs(r) different symbols, then one can come up with many representations (Ofcourse all these representations need not have a bijection with the natural numbers).

So in view of this,
we can sort of have a base 1 representation, the counting in this schema would be
a,aa,aaa,aaaa,aaaaa,...
(One can use any symbol instead of a and assign it the weight 1)
This is called as a unary representation. (This is highly useful in many analysis of Turing machines)

One can even have negative bases as well (! Now u see why i wrote abs(r) in my earlier definition :) ).
A very nice base and the one used infrequently is the base -2 representation. The symbols used for this representations are 0 and 1 with their usual weights 0 and 1.
e.g,
1 = 1
0 = 0
11 = -1
10 = -2
100 = 4
101 = 5
110 = 2
and so on...

-- AI

 

[The Bob]

One can even have negative bases as well (! Now u see why i wrote abs(r) in my earlier definition :) ).
A very nice base and the one used infrequently is the base -2 representation. The symbols used for this representations are 0 and 1 with their usual weights 0 and 1.
e.g,
1 = 1
0 = 0
11 = -1
10 = -2
100 = 4
101 = 5
110 = 2
and so on...

-- AI

Erm... am I the only one that doesn't understand this?

Sorry AI but I don't get it. Being slow again.

The Bob (2004 ©)

 

[4newton]

It depends on you profession.

If you are a mathematician you answer is 4

If you are an experimental physicist you will need to measure it.

If you are a theoretical physicist you will dream up some relative number.

If you are an account you will ask what do you want it to be.

 

[TenaliRaman]

Bob,
haven't got much time now ...
see if this helps,
abs(-2) = 2
so we can use two different symbols (say a and b and i will assign them values 0 and 1 but why not we use 0 and 1 themselves as symbols ... so we use 0 and 1 as symbols instead of a and b)

now 110 in base -2 ... so in base 10 it would be,
1*(-2)^2 + 1*(-2) + 0 = 2

so we see that 110 in base -2 is 2 in base 10

in this way numbers can be represented in base -2 ...

if any problems post again and i will try to detail things out...

-- AI

 

[The Bob]

Bob,
haven't got much time now ...
see if this helps,
abs(-2) = 2
so we can use two different symbols (say a and b and i will assign them values 0 and 1 but why not we use 0 and 1 themselves as symbols ... so we use 0 and 1 as symbols instead of a and b)

now 110 in base -2 ... so in base 10 it would be,
1*(-2)^2 + 1*(-2) + 0 = 2

so we see that 110 in base -2 is 2 in base 10

in this way numbers can be represented in base -2 ...

if any problems post again and i will try to detail things out...

-- AI

I believe I understand but I will have to do some in my own time and post again.

Cheers for the help :thumbs_up

The Bob (2004 ©)

 

[Learning Curve]

... our number system is in base 10; 10,20,30...
... binary code is in a base 2; 01,010,
Base is the number of digits one number place can hold.