Because we should be working with labelled sequences rather than just sequences (that is sequences with a length attached). That solves the most obvious issues, though there are some subtleties there
Why? Plain sequences are a perfectly natural object of study. I’ll echo gjm’s criticism that you seem to be trying to “resolve” paradoxes by changing the definitions of the words people use so that they refer to unnatural concepts that have been gerrymandered to fit your solution, while refusing to talk about the natural concepts that people actually care about.
I don’t think think your proposal is a good one for indexed sequences either. It is pretty weird that shifting the indices of your sequence over by 1 could change the size of the sequence.
Because we should be working with labelled sequences rather than just sequences (that is sequences with a length attached). That solves the most obvious issues, though there are some subtleties there
Why? Plain sequences are a perfectly natural object of study. I’ll echo gjm’s criticism that you seem to be trying to “resolve” paradoxes by changing the definitions of the words people use so that they refer to unnatural concepts that have been gerrymandered to fit your solution, while refusing to talk about the natural concepts that people actually care about.
I don’t think think your proposal is a good one for indexed sequences either. It is pretty weird that shifting the indices of your sequence over by 1 could change the size of the sequence.