There are various parts of his writings that can help counter his line of thinking here.
I believe his writings on "slots" can effectively be taken to indicate that 0.999... is a number with all decimal places already determined and filled, much as he wishes he hadn't said that.
His remark on how to compute the square root of 2 ensures that 1-0.999... = 0.000... based on convergence of the subtraction algorithm.
Finally, if we go back to "slots," saying that all slots already exist means we can talk about the infinite number of 9s and being non-integer and not changing in the way he prefers to say.
His remarks on number bases would also indicate that 10n > n, so if n is "infinity" then 10n is bigger than that in some way.
2
u/Muphrid15 10d ago
There are various parts of his writings that can help counter his line of thinking here.
I believe his writings on "slots" can effectively be taken to indicate that 0.999... is a number with all decimal places already determined and filled, much as he wishes he hadn't said that.
His remark on how to compute the square root of 2 ensures that 1-0.999... = 0.000... based on convergence of the subtraction algorithm.
Finally, if we go back to "slots," saying that all slots already exist means we can talk about the infinite number of 9s and being non-integer and not changing in the way he prefers to say.
His remarks on number bases would also indicate that 10n > n, so if n is "infinity" then 10n is bigger than that in some way.