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        riddles >> medium >> changing the fundamentals to Math and its cons.
        
(Message started by: BMAD on May 24^th, 2014, 7:21am)

Title: changing the fundamentals to Math and its cons.
Post by BMAD on May 24^th, 2014, 7:21am

1. numerical value is comprised of set of one equal to that value
2. All numerical values should be written in a sequence using a comma to separate all numbers.
3. the addition of two numerical values is the listing of both sets of ones join by a comma.
4. The solution to an addition problem is the count of commas.
E.g.
5 = {1,1,1,1,1}
6 ={1,1,1,1,1,1}
5+6 = {1,1,1,1,1 , 1,1,1,1,1,1} = 10 (because there are 10 commas)

5. All other mathematical operations are linked to addition in the manner as it was before.

Solve:

1+0=
8 - 5 =
3 × 5 =
1 2 / 4 =
Sqrt (36)
3+5×2=
3x-6 = 21, x =
Derivative of 3x
Anti derivative of 3x

Title: Re: changing the fundamentals to and its consequ
Post by BMAD on May 24^th, 2014, 7:28am

When i say linked to addition I mean
Multiplication can be considered repeated addition.
Subtraction can be written as an equivalent addition statement
Division is repeated subtraction
And so on

Title: Re: changing the fundamentals to Math and its cons
Post by BMAD on May 25^th, 2014, 8:07am

1 + 0 = {1} = 0 (no commas)

Title: Re: changing the fundamentals to Math and its cons
Post by towr on May 25^th, 2014, 10:59am

8 - 5 = 4

Title: Re: changing the fundamentals to Math and its cons
Post by dudiobugtron on May 25^th, 2014, 4:56pm

So, basically, each time you add, you subtract 1 from the normal total?

In that case, multiplication isn't commutative. 5 + 5 + 5 = 13 is different from 3 + 3 + 3 + 3 + 3 = 11.

So we need to know which of those 3 x 5 means.

Title: Re: changing the fundamentals to Math and its cons
Post by BMAD on May 25^th, 2014, 10:53pm

on 05/25/14 at 16:56:33, dudiobugtron wrote:

Not quite:

5x3 would be either

5 ={1,1,1,1,1}
3= {1,1,1}

So 5 x 3 = 5 + 5 +5 or = 3 + 3 + 3 + 3 + 3

5 case= {1,1,1,1,1 , 1,1,1,1,1 , 1,1,1,1,1} = 14
3 case={1,1,1 , 1,1,1 , 1,1,1 , 1,1,1 , 1,1,1} = 14

So remember it is the count of commas.

Title: Re: changing the fundamentals to Math and its cons
Post by towr on May 25^th, 2014, 11:20pm

The trouble is that means there's a difference between 5 + 5 +5 and (5 + 5) + 5. So how does that affect other sums with multiple operations?
Do we have
3 + 5 × 2 = 3 + (5 × 2) = 3 + 9 = 11
or
3 + 5 × 2 = 3 + 5 + 5 = 12
?

Title: Re: changing the fundamentals to Math and its cons
Post by BMAD on May 25^th, 2014, 11:25pm

To me in this set of rules. .. The order of operations do not get resolved step wise but in one swoop, the order just gives structure to which ones get combined first. Which shouldn't change the answers.

Title: Re: changing the fundamentals to Math and its cons
Post by dudiobugtron on May 26^th, 2014, 12:04am

12 / 4 :
9 + 4 = 12 so 12 - 4 = 9
5 + 4 + 4 = 12 so 12 - 4 - 4 = 5
similarly 12 - 4 - 4 - 4 = 1

So I guess that means 12 / 4 = 3 remainder 1.

PS: re order of operations:
[hide]What towr meant (I imagine) wasn't specifically about brackets and how to interpret them. It's that if you do 5 + 5 first, then take that answer and add 5 again, the answer you get is different from 5 + 5 + 5.[/hide]

Title: Re: changing the fundamentals to Math and its cons
Post by rmsgrey on May 26^th, 2014, 7:30am

So 2={1,1}
1={1}
1+1={1 , 1}=1

So {1} = {1 , 1} =/= {1,1}

???

Title: Re: changing the fundamentals to Math and its cons
Post by BMAD on May 26^th, 2014, 7:34am

In this world, 1 is the additive identity.
So 8 + 1 = 8, 1 + 1 =1 and so on.

Title: Re: changing the fundamentals to Math and its cons
Post by dudiobugtron on May 26^th, 2014, 3:12pm

sqrt(36) isn't defined. There is no number x where you can add it to itself x times to get 36.
6+6+6+6+6+6 = 35
7+7+7+7+7+7+7 = 48
so sqrt(35) = 6, but sqrt(36) isn't defined.

Unless you have a way of representing 'un-natural' numbers, you can't sqrt 36.

on 05/26/14 at 07:30:04, rmsgrey wrote:

So 2={1,1}
1={1}
1+1={1 , 1}=1

So {1} = {1 , 1} =/= {1,1}

???

1 + 1 doesn't actually equal {1 , 1}; you just have to create the construction {1 , 1} in order to work it out.

Title: Re: changing the fundamentals to Math and its cons
Post by towr on May 26^th, 2014, 10:08pm

Maybe sqrt(36) = 5

{1,1,1,1,1,1,
1,1,1,1,1,1,
1,1,1,1,1,1,
1,1,1,1,1,1,
1,1,1,1,1,1,
1,1,1,1,1,1} -[ sqrt ] -> {1,1,1,1,1,1} -[=]-> 5

Title: Re: changing the fundamentals to Math and its cons
Post by BMAD on May 27^th, 2014, 5:09am

Interestingly I had the same answer for sqrt (36) as tower originally considering it only a geometric interpretation. I failed to consider it a arithmetic interpretation like dudiobugtron. So I think they may be right in labeling this as undefinable given its two possible solutions (and even others may still exist).

Title: Re: changing the fundamentals to Math and its cons
Post by dudiobugtron on May 27^th, 2014, 6:48pm

In that case, I'm not entirely sure how to solve:
3x-6 = 21

I was going to solve it by rearranging:
3x = 21 + 6
3x = 26
x = 26 / 3
x = 9 (because 9 + 9 + 9 = 26 )

Is that what you had in mind?

-------------------------------------------
Also I think the derivative question is interesting. Of course, since there are no in-between numbers, the graph of y = 3x is not anywhere continuous, and so can't really be differentiated.

But assuming we're allowed to 'connect the dots' for the purposes of differentiating, then:

The graph of y = 36 looks exactly like the normal graph of y = 3x - 1.
So, in that case, you'd think the gradient would be 3; since the slope is the same. However, it depends on how you define the gradient. If it is something like 'rise over run', then the formula might be:

(y₂ - y₁) / (x₂ - x₁)

when x = 2, y = 5
when x = 3, y = 8

So the gradient from 2 to 3 is:
( 8 - 5 ) / ( 3 - 2)
= 4 / 2
= 2 remainder 1. (since 2 + 2 = 3, but 2 + 2 + 1 = 4)

Let's pick a different point:

when x = 1, y = 2
Then, the gradient from 1 to 3 is:
(8 - 2) / (3 - 1)
= 7 / 3
= 2 remainder 2.

So it looks like defining the gradient that way doesn't always give the same answer. Anyone have any ideas on how to do it consistently?

Title: Re: changing the fundamentals to Math and its cons
Post by BMAD on May 27^th, 2014, 7:00pm

Yes.