Found out 200 + 200 = 5. How?

Originally posted by leisurelysloth
Does 200 = 200 or are these in different bases as well? It would seems that there might be multiple "correct" answers.

EDIT: If 200 = 200, then 200 = 2.5,
or 100 = 1.25 or 5/4, so it would seem that the base is (5/4)^0.5

This would be an odd counting system, however, as:

100 = 1.25
200 = 2.5
1000 = ~1.4

200 > 1000 ???

Or perhaps my math is wrong.... 😞 It's been about 1000 years since I took any math classes! 😵

You are sniffing around the right bush anyway. One hint:
the 5 in base ten is exact. That was the suprise for me. Its the only one that is, at least at the depth at which I looked. That is to say, 100 to 900 will return exact numbers, but not 10 through 90 for instance.

Originally posted by sonhouse
You are sniffing around the right bush anyway. One hint:
the 5 in base ten is exact. That was the suprise for me. Its the only one that is, at least at the depth at which I looked. That is to say, 100 to 900 will return exact numbers, but not 10 through 90 for instance.

So, does 200 = 200? Are the first two numbers in the same base?

Originally posted by leisurelysloth
So, does 200 = 200? Are the first two numbers in the same base?

Absolutely! Exactly the same base, But the base is my invention, or my realization anyway, I don't think anyone else ever used it before to represent numbers. I came across it after XanthosNZ made a statement to the effect that 2+2 = 5 for sufficiently large 2's or something like that. I searched for a way to make that happen. Didn't do it for that one exactly but found one for 200+200=5(base 10).
So your mission, should you chose to accept it, is to find the exact base that satisfies that little equation.

An even number + an even number always gives an even number.
An odd number + an odd number also always gives an even number.
So two same numbers added must give an even number.

5 is clearly odd then 200+200 never gives 5, no matter what base.

If 200+200=5 then you have to use your own diefinitions or own handicrafted rules. And then this is not regular math.

Since 200 + 200 (in some base 'n'😉 = 5 (base 10)
then clearly 200 (base n) = 2.5
so 2 * n^2 + 0 * n + 0 = 2.5
which simplifies to n^2 = 1.25
hence n = sqrt(1.25)
= sqrt(5/4)
= sqrt(5) / 2

The sqrt(5) immediately brings phi to mind, and it turns out than n is equaly to phi - 0.5.

Originally posted by Fat Lady
Since 200 + 200 (in some base 'n'😉 = 5 (base 10)
then clearly 200 (base n) = 2.5
so 2 * n^2 + 0 * n + 0 = 2.5
which simplifies to n^2 = 1.25
hence n = sqrt(1.25)
= sqrt(5/4)
= sqrt(5) / 2

The sqrt(5) immediately brings phi to mind, and it turns out than n is equaly to phi - 0.5.

You get the brass ring! That was what I was trying to hint at to Fabian, the base does not have to be an integer. Did you ever hear of a book by Malcom Lines called 'A number for your thoughts'? He is a friend, a scientist from Bell Labs who worked at our little startup, Inplane Photonics in New Jersey and I talked with him quite a bit about math and science in general and he gave me a copy of that little book. What was interesting in it was the idea that the base doesn't even have to be positive numbers, it can also be based on negative numbers! Isaac Asimov read that and was blown away and they corresponded for years till Isaac died.
In this problem, the third digit was the only one I found to contain an exact numerical representation. Going up and down the power series, the rest (at least the ones I checked) to not be exact like that, I wonder if there is another power up the line that is exact also?
But at any rate, Great Job!
Very close to phi, phi being 1/2+(5^0.5/2) and 1/2-(5^0.5/2)
I wonder what the properties of numbers would be like if phi was used as a base?

I object!

If you consider 200+200=5 is a true statement - you use either kindergaren math or over the top university high shot math. In either case you can prove any ridicules just by using weird rules (which of course is perfectly sound in the right environment, kindergarten or over the top university high shot math).

BTH - does this mean that even + even can be an odd sum? And odd odd can be odd as well? Nooo, I don't beleive it...

I object!

Originally posted by FabianFnas
I object!

If you consider 200+200=5 is a true statement - you use either kindergaren math or over the top university high shot math. In either case you can prove any ridicules just by using weird rules (which of course is perfectly sound in the right environment, kindergarten or over the top university high shot math).

BTH - does this mean that even ...[text shortened]... ven can be an odd sum? And odd odd can be odd as well? Nooo, I don't beleive it...

I object!

You need to read 'A number for your thoughts' by my buddy Malcom Lines. It shows a lot of stuff that seems counter-intuitive like number bases that use negative numbers and such! Did you get my PM about Sune?

Originally posted by sonhouse
In this problem, the third digit was the only one I found to contain an exact numerical representation. Going up and down the power series, the rest (at least the ones I checked) to not be exact like that, I wonder if there is another power up the line that is exact also?

Sorry, I don't understand this.

Originally posted by sonhouse
You get the brass ring! That was what I was trying to hint at to Fabian, the base does not have to be an integer. Did you ever hear of a book by Malcom Lines called 'A number for your thoughts'? He is a friend, a scientist from Bell Labs who worked at our little startup, Inplane Photonics in New Jersey and I talked with him quite a bit about math and scienc ...[text shortened]... 2-(5^0.5/2)
I wonder what the properties of numbers would be like if phi was used as a base?

Have another *bonk* for your collection! 🙄

Originally posted by sonhouse

I wonder what the properties of numbers would be like if phi was used as a base?

Well, one of the many interesting identities involving phi is that phi*phi = phi + 1. In base phi this would become:

100 = 11

Originally posted by Fat Lady
Well, one of the many interesting identities involving phi is that phi*phi = phi + 1. In base phi this would become:

100 = 11

So we have just invented Hi-phi math, eh! Gimmee a Hi-phi!
I like it! But how is 100=11? If its Phi^2, shouldn't it be 2.6 something? Isn't phi 1.6ish? And -0.6something too, there are two solutions for phi if I have it right. .5+ 5^.5/2 and .5-5^.5/2 right?

Originally posted by sonhouse
So we have just invented Hi-phi math, eh! Gimmee a Hi-phi!
I like it! But how is 100=11? If its Phi^2, shouldn't it be 2.6 something? Isn't phi 1.6ish? And -0.6something too, there are two solutions for phi if I have it right. .5+ 5^.5/2 and .5-5^.5/2 right?

Phi is usually described as 1.618034 (roughly).

In the equation 100 = 11, both sides are in base phi.

The left hand side is equal to 1 * phi^2 + 0 * phi + 0 = phi^2
The right hand side is equal to 1 * phi + 1 = phi + 1

In the same way, 1/phi is equal to phi - 1, which in base phi would be:

0.1 = 10 - 1

Originally posted by sonhouse
I hear the taxes in Ireland are 55%.

You hear wrong.

D

Originally posted by Ragnorak
You hear wrong.

D

Too high or too low?