Surreal edition
Previous thread: >>14036109
Discuss the properties of the mysterious number 0.999... and its elusive relationship with one. Not much is known about 0.999... and I hope to encourage civil discussion to push the limits of our collective knowledge on this topic.
>What's so interesting about 0.999...?
In recent decades, the study of 0.999... has led us to a number of discoveries and applications in unexpected places, such as differential geometry and combinatorial game theory. 0.999... remains an active research topic and a treasure trove of mathematical insight, but there is still so much we have to learn about 0.999....
Central to the study of the 0.999... is perhaps one of the most important unanswered questions of mathematics: the unity conjecture. The unity conjecture states that 0.999... = 1. As of now the unity conjecture remains to be proven or disproven in any definitive way.
>Isn't 0.999... already proven to be equal to 1?
There are many naive proofs circulating online that 0.999... = 1. But there is still a lot of debate on this topic, so the issue is not settled. Many of these naive proofs have been debunked.
>You can obviously tell 0.999... is less than 1, just by the way it's written.
Numbers are not necessarily as they seem. 1.0 is equal to 1, even though they are written differently. There are easy ways to show that 1.0 = 1, but the case of 0.999... is not so trivial.
>I have proven/disproven the unity conjecture!
Feel free to share your results here, and your peers will debate the validity of your argument.
Previous thread: >>14036109
Discuss the properties of the mysterious number 0.999... and its elusive relationship with one. Not much is known about 0.999... and I hope to encourage civil discussion to push the limits of our collective knowledge on this topic.
>What's so interesting about 0.999...?
In recent decades, the study of 0.999... has led us to a number of discoveries and applications in unexpected places, such as differential geometry and combinatorial game theory. 0.999... remains an active research topic and a treasure trove of mathematical insight, but there is still so much we have to learn about 0.999....
Central to the study of the 0.999... is perhaps one of the most important unanswered questions of mathematics: the unity conjecture. The unity conjecture states that 0.999... = 1. As of now the unity conjecture remains to be proven or disproven in any definitive way.
>Isn't 0.999... already proven to be equal to 1?
There are many naive proofs circulating online that 0.999... = 1. But there is still a lot of debate on this topic, so the issue is not settled. Many of these naive proofs have been debunked.
>You can obviously tell 0.999... is less than 1, just by the way it's written.
Numbers are not necessarily as they seem. 1.0 is equal to 1, even though they are written differently. There are easy ways to show that 1.0 = 1, but the case of 0.999... is not so trivial.
>I have proven/disproven the unity conjecture!
Feel free to share your results here, and your peers will debate the validity of your argument.
