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 changing the fundamentals to Math and its cons.   « on: May 24th, 2014, 7:21am » Quote Modify

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
 « Last Edit: May 24th, 2014, 8:50am by BMAD » IP Logged
Junior Member

Posts: 57
 Re: changing the fundamentals to  and its consequ   « Reply #1 on: May 24th, 2014, 7:28am » Quote Modify

Multiplication can be considered repeated addition.
Subtraction can be written as an equivalent addition statement
Division is repeated subtraction
And so on
 « Last Edit: May 24th, 2014, 8:50am by BMAD » IP Logged
Junior Member

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 Re: changing the fundamentals to Math and its cons   « Reply #2 on: May 25th, 2014, 8:07am » Quote Modify

1 + 0 = {1} = 0 (no commas)
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towr
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 Re: changing the fundamentals to Math and its cons   « Reply #3 on: May 25th, 2014, 10:59am » Quote Modify

8 - 5 = 4
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dudiobugtron
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 Re: changing the fundamentals to Math and its cons   « Reply #4 on: May 25th, 2014, 4:56pm » Quote Modify

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.
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 Re: changing the fundamentals to Math and its cons   « Reply #5 on: May 25th, 2014, 10:53pm » Quote Modify

on May 25th, 2014, 4:56pm, dudiobugtron wrote:
 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.

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.
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towr
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 Re: changing the fundamentals to Math and its cons   « Reply #6 on: May 25th, 2014, 11:20pm » Quote Modify

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
?
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 Re: changing the fundamentals to Math and its cons   « Reply #7 on: May 25th, 2014, 11:25pm » Quote Modify

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.
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dudiobugtron
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 Re: changing the fundamentals to Math and its cons   « Reply #8 on: May 26th, 2014, 12:04am » Quote Modify

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:
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.
 « Last Edit: May 26th, 2014, 12:10am by dudiobugtron » IP Logged
rmsgrey
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 Re: changing the fundamentals to Math and its cons   « Reply #9 on: May 26th, 2014, 7:30am » Quote Modify

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

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

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 Re: changing the fundamentals to Math and its cons   « Reply #10 on: May 26th, 2014, 7:34am » Quote Modify

In this world, 1 is the additive identity.
So 8 + 1 = 8, 1 + 1 =1 and so on.
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dudiobugtron
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 Re: changing the fundamentals to Math and its cons   « Reply #11 on: May 26th, 2014, 3:12pm » Quote Modify

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 May 26th, 2014, 7:30am, 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.
 « Last Edit: May 26th, 2014, 3:15pm by dudiobugtron » IP Logged
towr
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 Re: changing the fundamentals to Math and its cons   « Reply #12 on: May 26th, 2014, 10:08pm » Quote Modify

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
 « Last Edit: May 26th, 2014, 10:09pm by towr » IP Logged

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Junior Member

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 Re: changing the fundamentals to Math and its cons   « Reply #13 on: May 27th, 2014, 5:09am » Quote Modify

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).
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dudiobugtron
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 Re: changing the fundamentals to Math and its cons   « Reply #14 on: May 27th, 2014, 6:48pm » Quote Modify

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?
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 Re: changing the fundamentals to Math and its cons   « Reply #15 on: May 27th, 2014, 7:00pm » Quote Modify

Yes.
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