You should be careful with addition and multiplication - to use them, you would have to define them first, and this is not trivial if you have the natural numbers plus A->B->C->A, infinite chains and so on.
In addition, "group" has a specific mathematical meaning, if you use it for arbitrary sets this is quite confusing.
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My predictions to these topics: No experiment apart from OPERA will measure a neutrino speed >c with a significance of more than 3 sigma in 2012: 85% - where the 15% are mainly related to measurement errors OPERA or others will find a significant error in OPERAs measurements in 2012: 50%
Higgs boson will be seen with a local 5 sigma significance (ATLAS+CMS alone or in combination) near ~125 GeV in 2012: 90% - the current signal is quite clear already, even without the magic 5 sigma. So I expect that new data will increase the significance. From the 10%, a large part is related to possible problems with the LHC, it includes serious analysis problems, bad luck and the simple "there is no higgs". Higgs boson will be seen with a global 5 sigma significance (ATLAS+CMS alone or in combination) near ~125 GeV in 2012: 85% - this needs a bit more data than the local significance.
No other new particles will be seen with 5 sigma significance in 2012: 75% - up to now, I did not see any hint for a new particle from both collaborations, so I think there is no 3sigma evidence for anything at the moment
The LHC will collide protons with lead at the end of 2012: 75% - it was tested in 2011, but technical problems prevented collisions
Let's see.
From the other comment with predictions: