Yaroslav D. Sergeyev and the Infinity1
I reckon the theory grossone as a very attractive model because it tries to break Cantor’s concept of infinity. My problems related to Cantor's model of infinity could best articulate the my critique of his diagonal method.2 According to Cantor’s notion of infinity the part may be equal to the whole. The author of the grossone theory Sergeyev sees this as the inadequacy of Cantor’s model because this contradicts our intuitive approach as we observe it all around us that the part is less than the whole. Based on this intuitive insight the grossone model postulates that the part is less than the whole for the infinities as well. So Cantor's criticism of Sergeyev is not based on a mathematical basis, but the so-called common sense approach.
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1 See for example the following articles and a book: http://arxiv.org/pdf/1203.4141v1.pdf , http://arxiv.org/pdf/1203.3132v1.pdf ,http://www.amazon.co.uk/Arithmetic-infinity-Yaroslav-D-Sergeyev/dp/8889064013
2 See for example the following article "Problems with the use of Cantor’s diagonal argument"
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