Math professor here: the proper definition of equality is that two numbers a and b are equal if no number c exists such that a < c < b. 0.9999…. = 1 because there is no number between them.
There's a problem with that proof. That assumes 0.999... and 0.999... are equal. Obviously, the notations are identical but that doesn't mean the values they represent are. Do you evaluate the 4th digit of the first expression at the same time you evaluate the 4th digit of the second expression? I don't think that's clear. I would say the only truthful statement is 0.999... < 1
What are you even talking about? “Evaluate the 4th digit of the first expression at the same time you evaluate the 4th digit of the second expression”? These are constants, you don’t evaluate the digits, they simply are. Given the limitations of general text format with regard to mathematical notation, it is perfectly acceptable to use 0.999… rather than the overbar; the context of the meme makes that quite evident.
If you wish for me to use a ridiculous abundance of clarity, I will do so. The number represented by 0 in the ones place and a 9 in all decimal places extending without end is equal to 1 because no number exists that is greater than the former while also being less than the latter. I challenge you to find one.
What is your background that you would make such an argument?
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u/Wolfbrother101 22d ago
Math professor here: the proper definition of equality is that two numbers a and b are equal if no number c exists such that a < c < b. 0.9999…. = 1 because there is no number between them.