More generally, don’t assume that the same word means the same thing in different fields. Although, in this case, I’d say it’s the mathematician’s fault for being so incredibly obtuse.
But what about your friend and Cantor’s argument? Was she confusing the “size” infinities with the “limit” infinities?
She was indeed confusing those two infinities, so couldn’t grasp how there could be different sizes—a singularity/pole that rises faster to infinity, is still just a singularity, so it made no sense to her that infinities could be bigger than each other.
Because she wasn’t thinking of infinity as being a list or a set (she wasn’t thinking of cardinal infinities). So any list-based method seemed an illegitimate way of talking about infinity. (oh, and she was certainly willing to believe that the proof was correct—she didn’t think all those mathematicians throughout the ages were wrong! She just didn’t understand it).
More generally, don’t assume that the same word means the same thing in different fields. Although, in this case, I’d say it’s the mathematician’s fault for being so incredibly obtuse.
But what about your friend and Cantor’s argument? Was she confusing the “size” infinities with the “limit” infinities?
She was indeed confusing those two infinities, so couldn’t grasp how there could be different sizes—a singularity/pole that rises faster to infinity, is still just a singularity, so it made no sense to her that infinities could be bigger than each other.
Why did Cantor’s diagonalisation not make it make sense to her, or at least show her that whatever was right, her intuition was wrong?
Because she wasn’t thinking of infinity as being a list or a set (she wasn’t thinking of cardinal infinities). So any list-based method seemed an illegitimate way of talking about infinity. (oh, and she was certainly willing to believe that the proof was correct—she didn’t think all those mathematicians throughout the ages were wrong! She just didn’t understand it).