Agreed. In that sense, I obviously accept the notion
of “distinct infinities“, cf me talking “projective.”
Maybe, for consistency’s sake, such a comparison should
issue an error; for practical purposes I guess it’s quite
okay the way it is?
nuff said, I leave this for the better informed to decide
Am 23.02.22 um 17:58 schrieb Elijah Stone:
When I said 'two infinities' I meant 'two values, both of which are
infinite'.
For instance, _ and __ are both infinite, though they happen to be
unequal. In this case I meant to distinguish values such as 3j_ and
5j_; they are both infinite, and they should perhaps compare equal, but
they are also clearly distinct in some sense.
-E
On Wed, 23 Feb 2022, Hauke Rehr wrote:
this juxtaposition of words is incomprehensible to me
_ is one exact value: the limit of any sequence growing unboundedly
this one exact value is equal to itself no matter the sequence
adding sequences diverging towards _ and __ doesn’t lead to a single
defined result → NaN, same goes for subtracting two sequences both
diverging towards _
So I consider both + and = consistent with what my prejudice is
concerning the identity of that well defined value _
Am 23.02.22 um 17:44 schrieb Elijah Stone:
two infinities
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