Your question can be interpreted in 2 ways with different answers. Non uniques representation exits in every number system. For example is in the decimal system 1=0.9999..... But there is another easier way of fixing this proof than shown in this video by using other number systems. Let use our binary sequence with another system than the binary system, for example the decimal system. Then all representations are unique and we can directly use the diagonal argument to show, that there is not 1-zo-1 correspondece to a true subset on [0,1].
0.25=0.249999999... Yes The thing is, it's not a problem. It's just a conquense of any number line being continuous. Look up 1=0.999... 0.9999... is the decimal representation of 1 and are equal. This has been proven many different ways mathematically and logically, so don't listen to anyone who tries to say otherwise.
Genuinely very interesting! I tried working through the proof on my own and was stumped at the point where I had to form a unique correspondence using a non-unique representation. I hadn't thought of just shifting it over LOL.
Wait I just realized something. This video saying there is problem somehow when there is not. I think. Or it's just stating that a number can have 2 representations, which is again, is not a problem. Anyway 0.1 and 0.0111... are the exact same number and are equal like 1=0.999... It is not a problem, but a consequence of number lines being continuous. They are the exact same number and this is has been proven mathematically and logically and there is no changing that fact.
@@penguincute35640.9999... is the decimal representation of 1. They are equal and this has been proven mathematically and logically. Don't listen to anyone who tries to say otherwise.
I thought an english channel already existed and I just now discovered it. instead it's brand new!
very cool, I instantly subbed
Amazing! Zundamon sounds very good! Metan sounds a little bit more robotic, but it's still good. Thanks a lot for the english dub
Nice video. The shifting argument at the end is also exactly how Cantor derived a bijection between Z+ and Q.
Third subscriber, let's gooo. In all seriousness tho, I'm happy that you made an English channel, I love your videos
is the non uniqe representation problem occur only in binary? wouldn't it show up in other number systems as well?
Your question can be interpreted in 2 ways with different answers. Non uniques representation exits in every number system. For example is in the decimal system 1=0.9999.....
But there is another easier way of fixing this proof than shown in this video by using other number systems. Let use our binary sequence with another system than the binary system, for example the decimal system. Then all representations are unique and we can directly use the diagonal argument to show, that there is not 1-zo-1 correspondece to a true subset on [0,1].
0.25=0.249999999...
Yes
The thing is, it's not a problem. It's just a conquense of any number line being continuous. Look up 1=0.999...
0.9999... is the decimal representation of 1 and are equal. This has been proven many different ways mathematically and logically, so don't listen to anyone who tries to say otherwise.
Good old voiceroid.🐾
Glad you are doing english dubs too
As long as there isn't infinite repeated digits there will be a pne to one representation
Holy moly
Genuinely very interesting! I tried working through the proof on my own and was stumped at the point where I had to form a unique correspondence using a non-unique representation. I hadn't thought of just shifting it over LOL.
この人英語版も作ってたのか
英語版作ったんですね！
Very cool that you made a English dub for the channel! It is very appreciated, although I'll keep watching the jp channel with the english subbtitles
1:03
small mistake here: there is no number between 0 and 1 it is just 0 and 1
so, [0, ... , 1] not {0, ... , 1}.
btw, we are considering that {0 -> 1} and [0 -> 1] cannot contain reals.
Wait I just realized something. This video saying there is problem somehow when there is not. I think. Or it's just stating that a number can have 2 representations, which is again, is not a problem.
Anyway 0.1 and 0.0111... are the exact same number and are equal like 1=0.999... It is not a problem, but a consequence of number lines being continuous. They are the exact same number and this is has been proven mathematically and logically and there is no changing that fact.
i love this channel
the reason why 0.0111111111111111111111111111111111111111111...[2] = 0.1[2] is just the same reason why
0.99999999999999999999999...[10] = 1[10]
And that is caused by that 3/3 is 0.33… * 3 which should be 0.99… but is instead 1 because that’s just how it works.
@@penguincute35640.9999... is the decimal representation of 1. They are equal and this has been proven mathematically and logically. Don't listen to anyone who tries to say otherwise.
Thank youtube alg guide me to this, so impressive XD
New video😍
nice
Holy moly
nice