Whilst it's clear that many people wont accept that fact that 0.9r and 1 are exactly the same real number, it is unclear why such people would hold their own opinion in such high regard. For me, it's not about trying to convince people of the fact 1=0.9r - whether they understand it or not doesn't bother me. What irritates me is that they seem to think they know better.
I don't want to refer to the article I brought up, regarding incompetency, as it seemed to get peoples backs up. I shall simply state there are two different types of people I have encountered when it comes to this subject:
a) The people that find the result "1=0.9r" strange, and against their intuition. And then defer to the fact that they don't have more than an A-Level in mathematics (or less), so are willing to accept the result as true, but not as something they understand.
b) The people that find the result "1=0.9r" strange, and against their intuition. And then assert that because they don't get it, it must be wrong. Heaven forbid that their A in GCSE mathematics has not equipped them with the tools needed to understand the construction of the real numbers. No, it's not that. It's far more likely that all the worlds mathematicians, who have spent their lives studying the subject and probing the limits of our knowledge, missed this little bit.
I might add, that if any of the nay-sayers were correct, in that they had a proof that 1 and 0.9r were different real numbers, this would amount to finding an inconsistency in ZFC, which would undoubtedly lead to a Fields medal, the highest accolade any mathematician can amount to. Professorships, fellowships, research grants and a host of other financially beneficial offers would be bestowed upon you - so I would urge you to send your proofs to the leading journals.
I don't want to refer to the article I brought up, regarding incompetency, as it seemed to get peoples backs up. I shall simply state there are two different types of people I have encountered when it comes to this subject:
a) The people that find the result "1=0.9r" strange, and against their intuition. And then defer to the fact that they don't have more than an A-Level in mathematics (or less), so are willing to accept the result as true, but not as something they understand.
b) The people that find the result "1=0.9r" strange, and against their intuition. And then assert that because they don't get it, it must be wrong. Heaven forbid that their A in GCSE mathematics has not equipped them with the tools needed to understand the construction of the real numbers. No, it's not that. It's far more likely that all the worlds mathematicians, who have spent their lives studying the subject and probing the limits of our knowledge, missed this little bit.
I might add, that if any of the nay-sayers were correct, in that they had a proof that 1 and 0.9r were different real numbers, this would amount to finding an inconsistency in ZFC, which would undoubtedly lead to a Fields medal, the highest accolade any mathematician can amount to. Professorships, fellowships, research grants and a host of other financially beneficial offers would be bestowed upon you - so I would urge you to send your proofs to the leading journals.
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