However, this does provide the opportunity to think a bit more deeply about identity and being able to refer to a thing, like π.
To expand on this, the number n, like the number π, has no decimal representation, but unlike most real numbers, it is well-defined since it can be pointed to and thus named: the equation as given in the post is one such name (it is an implicit representation of n; simple algebra may be used to rewrite it into a more explicit form).
If n became useful enough, we could even give it a simpler name (like we did with π and 2), instead of the compound symbolic expression.
There are a lot of unspecified assumptions in Ender’s challenge, such as reducing the expression to some canonical form, e.g., 2 instead of 16⁄8, sqrt(4), or the only even prime number. It takes a bit of sophistication to appreciate the depth of questions of equality, identity, and representation.
The fact that Ender had not considered any of this while confidently presenting the challenge leaves me feeling a bit annoyed.
I’m kind of annoyed by the challenge, also.
However, this does provide the opportunity to think a bit more deeply about identity and being able to refer to a thing, like π.
To expand on this, the number n, like the number π, has no decimal representation, but unlike most real numbers, it is well-defined since it can be pointed to and thus named: the equation as given in the post is one such name (it is an implicit representation of n; simple algebra may be used to rewrite it into a more explicit form).
If n became useful enough, we could even give it a simpler name (like we did with π and 2), instead of the compound symbolic expression.
There are a lot of unspecified assumptions in Ender’s challenge, such as reducing the expression to some canonical form, e.g., 2 instead of 16⁄8, sqrt(4), or the only even prime number. It takes a bit of sophistication to appreciate the depth of questions of equality, identity, and representation.
The fact that Ender had not considered any of this while confidently presenting the challenge leaves me feeling a bit annoyed.