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1. (Original post by ZJuwelH)
<corrected error>

I refuse to accept it, there's a flaw somewhere, that ain't supposed to work...
Well if it is being taught by a 2:1 Cambridge graduate with over 20 years of teaching experience behind him, then I can't see any flaws in that can you?

I understand the hesitation, you think it might be similar to the trick that develops the 1 = 2 argument thingy, but rest assured, there is no problem. Do it yourself.
2. (Original post by ZJuwelH)
<corrected error>

I refuse to accept it, there's a flaw somewhere, that ain't supposed to work...
Also that way is a standard way of turing recurring decimals etc into a proper fraction. So it is a valid way of working things out.
3. (Original post by ZJuwelH)
<corrected error>

I refuse to accept it, there's a flaw somewhere, that ain't supposed to work...
there is a paradox. it is impossible to imagine that at any point this chain of digits, which by law is completely made up of nines to the point of infinity, is equal to anything else. but the algebra proves it.

If we construct a bulb such that it is on for 30 seconds, off fro 15, on for 7.5, off for 3.75 etc... after 1 minute is it off or on?
5. (Original post by theone)

If we construct a bulb such that it is on for 30 seconds, off fro 15, on for 7.5, off for 3.75 etc... after 1 minute is it off or on?
Off, it would've malfunctioned after all those switches...
6. (Original post by mik1a)
there is a paradox. it is impossible to imagine that at any point this chain of digits, which by law is completely made up of nines to the point of infinity, is equal to anything else. but the algebra proves it.
I don't want to believe it. There must be something up with it. Never mind, soon someone will find a bigger contradiction in number theory and all mathematics will fall apart...
7. (Original post by ZJuwelH)
Off, it would've malfunctioned after all those switches...
hehe, assume it doesn't
8. (Original post by theone)

If we construct a bulb such that it is on for 30 seconds, off fro 15, on for 7.5, off for 3.75 etc... after 1 minute is it off or on?
Theoretically it would never reach 1 minute exactly, always some time before it, but never reaching 0.99999999999.......... minute as well.

Physically, the light bulb would be limited by the speed of the electrons. ie at really short speeds, it depends on whether there is enough time for a complete circuit to happen
9. (Original post by ZJuwelH)
I don't want to believe it. There must be something up with it. Never mind, soon someone will find a bigger contradiction in number theory and all mathematics will fall apart...
But mathematics are based on axioms of thinking that can not be refuted. ie 1 + 1 = 2
10. (Original post by theone)
hehe, assume it doesn't
Then the person turning it on and off would get a tired arm...
11. (Original post by 2776)
But mathematics are based on axioms of thinking that can not be refuted. ie 1 + 1 = 2
Yeah I know. Imagine if one of the axioms fell apart...

Do you think someone who destroyed maths would be hailed as a genius or public enemy number one? Well maybe not hailed but respected or acknowledged or something...

Probably never happen, maths is the only infallible thing in the world...
12. (Original post by ZJuwelH)
Yeah I know. Imagine if one of the axioms fell apart...

Do you think someone who destroyed maths would be hailed as a genius or public enemy number one? Well maybe not hailed but respected or acknowledged or something...

Probably never happen, maths is the only infallible thing in the world...
Apparently someone proved that 1+ 1 = 2.

And only a handful of people appreciate the arguments of it. I would start worrying if it didn't work.
13. (Original post by theone)

If we construct a bulb such that it is on for 30 seconds, off fro 15, on for 7.5, off for 3.75 etc... after 1 minute is it off or on?
This is essentially one of the paradoxes of infinity right? It is similar to this problem - You drop a ball from 1 metre say and after it has travelled 1/2 metre you see it has half to go. After it has travelled half the remaining distance ie another 1/4, it has 1/4 to go. This carries on infinitely with the ball always having half the remaining distance to travel therefore never hits the floor. This is mathematically the limit of the summation of 2^-n from 1 as n tends to infinity. The summation tends to the limit of 1.
14. (Original post by 2776)
Apparently someone proved that 1+ 1 = 2.

And only a handful of people appreciate the arguments of it. I would start worrying if it didn't work.
I think Russel did in the Principia. There is a proof that 2x2=4 in the tractatus by wittgenstein that uses some def function but it is hard.
15. (Original post by mik1a)
I just realised something.

What is 4.4444... to 2 decimal places?
when rounding you just look to the next one. i.e. the 3rd decimal place in your question. there is no paradox.
16. (Original post by 2776)
Apparently someone proved that 1+ 1 = 2.

And only a handful of people appreciate the arguments of it. I would start worrying if it didn't work.
What would you do?
17. (Original post by bono)
What would you do?
what's more worrying is if 1 =/= 1.
18. (Original post by elpaw)
what's more worrying is if 1 =/= 1.
How can you prove 1 + 1 = 2?

It just is!
19. (Original post by elpaw)
what's more worrying is if 1 =/= 1.
Is it true that there is a "proof" that states 1 = 2?
20. (Original post by bono)
Is it true that there is a "proof" that states 1 = 2?
there is a "proof" but not a proof.

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