A Counter-exampleQ. What do you get if you put 20 software developers in a room and shut the door?
A. A discussion like this one.
Mathematics is capable of embracing concepts that may or may not have any correspondence in the real world. From a Mathematician's perspective 0.9 recurring and 1.0 recurring are both mathematically equivalent in value to 1.
0.99999999... + 0.99999999... = 1.99999999...
*Sits back and waits for counterexamples...*
General / Off-Topic Does 0.999999999... =1?
- Thread starter AluminumAlloy
- Start date
Two numbers are the same if there is no real number that can come between them. There is no real number that fits between 0.9999... and 1. Ergo, they are the same number.
But I prefer the other version given above:
1/3 = 0.3333...
3* 1/3 = 0.9999...
1 = 0.9999...
But I prefer the other version given above:
1/3 = 0.3333...
3* 1/3 = 0.9999...
1 = 0.9999...
https://www.youtube.com/watch?v=x-fUDqXlmHM
Should help (or maybe not) as there are 3 algebraic sums you can do with the same logic as yours:
1) 0.99... = 1
2) ...999 = -1
3) ...999.999... = 0
Watch to blow your mind
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https://www.youtube.com/watch?v=PZRI1IfStY0
Floating point joys!
Floating point joys!
https://www.youtube.com/watch?v=x-fUDqXlmHM
Should help (or maybe not) as there are 3 algebraic sums you can do with the same logic as yours:
1) 0.99... = 1
2) ...999 = -1
3) ...999.999... = 0
Watch to blow your mind
Yup. Pretty much what I said in my previous post. Infinity in Mathematics turns out to be a somewhat flexible notion.
Just to throw a little something else into the pot.
1 is, amongst other things, a natural number.
0.99999... is real number
Between any distinct pair of natural numbers there is an infinite number of real numbers. Ok so far?
There is an infinite number of natural numbers. Which means that the number of reals is infinity^2 (sort of...).
In plain English, there are different levels of infinity.
Disclaimer: I've messed about with the theory a bit - it's not quite as simple as I've made it look...
Further reading
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Indeed - I subscribe to numberphile on YouTube and there are a couple of vids talking about infinity and the different kinds.
I enjoy melting my mind
(Yes, I followed you - aware of the different kinds of infinities when talking about number sets : beyond my level of school education but fascinating to learn all the same)
I enjoy melting my mind
(Yes, I followed you - aware of the different kinds of infinities when talking about number sets : beyond my level of school education but fascinating to learn all the same)
The margin of error when dividing into thirds is easily explained as the bit that comes away on the knife that nobody can lick off.
Problem solved. Back to work!
Problem solved. Back to work!
There is no "margin of error". A third is precisely a third. It is just a random happenstance that we use a decimal system which cannot display it in decimal notation without the use of periods. If we were using one of the other numeric systems that have indeed been used by humans in the past, like the base-12 system, 1/3 could easily be represented with decimals and no period at all.
It depends who yo ask.
My systems record the most popular answer as:
''Eh, you wot?''
My systems record the most popular answer as:
''Eh, you wot?''