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Unfolding Nature Shop: Unfolding Nature: Being in the Implicate Order

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Re: .999...(repeating) = 1 [Re: cortex]
    #11612179 -

Does anyone remember the Monty Hall Problem thread that popped up about 3-4 years ago? 

Some people initially can't seem to separate their intuitions about reality from the rules and definitions of formal systems, yet later when you've convinced them of the difference, they just claim that because formal systems are not reality itself, that they're worthless--that their intuitive version is much better. 

They're almost always wrong on both counts.  (For example, if you actually perform the monty hall experiment with real people and real choice, the outcomes match up to the statistics, not the intuitive result).  I remember people even debating the empirical results in that thread...

:facepalm:

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Re: .999...(repeating) = 1 [Re: ChuangTzu]
    #11612661 -

It seems the more you study a formal system like physics or mathematics, the more the results these systems give to problems becomes more and more intuitive.  I've only been studying math and physics for a few years really, and only formally for about a year.  Concepts like limits and derivatives are really clear and concrete once you understand them, and seem really simple when once you do.


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Re: .999...(repeating) = 1 [Re: ChuangTzu]
    #11613375 -

Some people initially can't seem to separate their intuitions about reality from the rules and definitions of formal systems

Yeah, it's a manifestation of the plague on Earth known as religion. Once someone like that has made up their mind, they entrench and no amount of evidence contradicting the beliefs they've invested emotional energy in will change their mind.

It makes me sad. We joke about it here with these math results and people who deny them despite being shown the unassailable steps of the proof, but the real world fallout of this kind of pathological rigid thinking is what gives rise suicide bombers and burkas. It's why I think the human race, most of which is religions and can barely even spell 'science' let alone understand it, is doomed.

The teaching of science and critical thinking to kids is out only hope, and that's not happening. Witness the rigid thinking that denies evolution and legislates the teaching of ignorance and mythology as fact to kids trying to learn biology. It would be funny if it wasn't true. :sad:


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Republican Values:

1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.

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Re: .999...(repeating) = 1 [Re: Diploid]
    #11614101 -

I came up with another way to show this for the deniers who know basic algebra. It shows the consequence if .9999999... repeating were not equal to 1.

To make it cleaner and easier to read, in the following let N = .9999999... repeating. The symbol != means "is not equal to".

Assume that the following is true:

1) N != 1

Then by multiplying both sides by 9 we get

2) 9 * N != 9 * 1

which simplifies to

3) 9 * N != 9

now add N to both sides and we get

4) (9 * N) + N != 9 + N

this simplifies to

5) 10 * N != 9 + N

Since 9 + N is the same thing as 9 + .9999999... line 5 simplifies to

6) 10 * N != 9.9999999...

and finally, since 10 * N is the same thing as 10 * .9999999 we get

7) 10 * .9999999... != 9.9999999...

Finally, since multiplying anything by 10 means the same as moving the decimal point to the right one place, 10 * .9999999... is equal to 9.9999999... which simplifies line 7 to

8) 9.9999999... != 9.9999999...

Since line 8 is not true, it follows that line 1 is not true either.

BTW, there are some clever proofs in the Wiki page on this.


--------------------
Republican Values:

1) You can't get married to your spouse who is the same sex as you.
2) You can't have an abortion no matter how much you don't want a child.
3) You can't have a certain plant in your possession or you'll get locked up with a rapist and a murderer.

4) We need a smaller, less-intrusive government.

Extras: Filter Print Post Top
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Unfolding Nature Shop: Unfolding Nature: Being in the Implicate Order

General Interest > Science and Technology
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