Kommentare
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If yo flicker a light really infinitely fast it has the appearance of staying on. Light in itself is just a wave travelling at a frequency so technically it's always flickering even if it's always on.
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But 2*S when S=1-1+1-1+1... is S+S so this is 1-1+1-1+1-...+1-1+1-1+1-1... it cannot go beyond the infinity so such notation makes no sense.
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in a super position of 0 and 1
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What about this?(1-1)+(1-1)+(1-1)+...+(1-1)=
=infinity×(1-1)=infinity×0
which is indefinite.
That product can be equal to 1, to 0 or even to 1/2. -
(sorry for my english)
So S= 1-1+1-1+1-1+1-1....= 0 or 1, depending on when you "stop" adding (+1 or -1)
And it sounds weird to "stop" adding, when you are adding infinitely, but it's quite easy to understand if you suppose that infinite has a kind limit (which sounds kinda strange..).
Then you try to calculate : 1-S
1-S = 1-(1-1+1-1+1-1+1-1...) = 1-1+1-1+1-1+1-1+1...
And you conclude saying that 1-S = S.
I really don't agree with you. In the first part, you suppose that there are 2 differents infinite but, in the second one you don't specify that, if S has an infinity of terms, 1-S has an infinity +1 of terms.
I hope I was clear, and please answer if you disagree with my reasoning and explain why I'm wrong. -
1-1+1-1+1-1+1-1+1-1+1...
+1-1+1-1+1-1+1-1+1-1...
=1 and =2(1-1+1-1+1-1+1-1+1...)
so
1=2(1-1+1-1+1-1+1-1+1-1+1-1+1...)
so
1-1+1-1+1-1+1-1+1-1+1-1...=1/2 -
what if you use one of those dimmer sliders? you can set those to a half
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The light would be off because eventually the switch would malfunction.
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1-1+1-1+1-1+1-1+1-1+1-1+1-1+1-1+1=(ends with +1)1...
...1+1-1=(ends with -1)0... -
1/2 is only a conceptual answer as infinity is only a concept and not something definite.
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Well. If you put the light bulb in a closed box, at the end of the 3 minutes the light is on, off and half on all at the same time. 🤗🤗🤗
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i don't see how any of this holds... I dont see the same equitation. i see three different equations. they all seem to have a different component that the other doesn't. Why SHOULD they all equal the same thing?
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Depends where you stop I guess.
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if you write S = 1-1+1-1+1-1... and, below it S = empty space +1-1+1-1..., you will get S=1/2, but if you write the same thing without the empty space, you should get S=0, right?
Why should the first version be more reliable than the second? -
this concept seems fundamentally wrong because the space of time in one minute is an infinite number of instances itsself
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The lamp state is not defined at the point of 2 mins and beyond due to way geometric series works.
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Probably by then the light bulb BREAKS away. Agreed?
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Brackets like this: (1-1) + (1-1) + .... Let c = (1-1). The series is then an infinite sum of c's: c + c + c + c + .... Or an infinite sum of 0's, which is 0.
Brackets like this: 1 + (-1 + 1) + (-1 + 1) + .... Let d = (-1 + 1). The series is then 1 + an infinite sum of d's: 1 + [d + d + d + d + ...]. Or 1 plus an infinite sum of 0's, which is 1.
These are 2 different series, not two different answers.
Now when he says let s = the series then does 1 - s, he is being ambiguous and not specifying which series is he subtracting from 1. There is no half. -
man first of all this series is not absolutely convergent hence we can't put brackets in different places.infact it is divergent series
11m 10sLänge
Discussing the brain-bending Grandi's Series and Thomson's Lamp - featuring Dr James Grime. A little bit of extra footage from the very end of this interview at: http://youtu.be/TgGi1ls1X-0 (on Brady's own channel) See our Zeno's Paradox video at http://youtu.be/u7Z9UnWOJNY Check computerphile at http://www.youtube.com/computerphile Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Google Plus: http://bit.ly/numberGplus Tumblr: http://numberphile.tumblr.com Videos by Brady Haran A run-down of Brady's channels: http://bit.ly/bradychannels