But is infinite information infinitely valuable?
Though both measures may be equally natural candidates for measuring the length of a proof, proving the theorem for length measured by the number of symbols avoids a technical complication introduced by the other measure: there are only finitely many proofs with a given number of symbols, whereas there are infinitely many proofs with a given number of formulas.
A modified view is presented by music writer Michael Steen, who questions whether "nationalistic music" can in fact exist: "We should recognise that, whereas music is infinitely expressive, on its own it is not good at describing concrete, earthly objects or concepts".
The first model assumes that the carrying cable is infinitely stiff, whereas the second model disregards the discrete character of the hangers.
The Aristotelian all, some, no are monotone in both arguments (e.g. all is right increasing and left decreasing), as are at least five, no more than ten, infinitely many, whereas most, at least two-thirds of the are right increasing but neither increasing nor decreasing in the left argument.
Consider a hypothetical subject who forgets the length of L1, but has no ambiguity about the length of L2, i.e., the neural representation of L1 is infinitely noisy whereas there is no noise in the neural representation of L2.
Analytical solutions are available for simple, infinitely long waveguides, whereas for more complex waveguides numerical approaches have been developed using finite element techniques to describe the cross-section.
Whereas in the plane there exist (in theory) infinitely many regular polygons, in three-dimensional space there exist exactly five regular polyhedra.
The first example is different from the last two in that it seems that we can know a priori that being such that there are infinitely many primes is essential to Socrates whereas it seems that we can know only a posteriori that being human and originating from s and e are also essential to him.
Whereas the commutation relations in QM refer to a quantum object with three degrees of freedom, so that one has a set of 15 equations, the commutation relations in QFT do in fact comprise an infinite number of equations, namely for each of the infinitely many space-time 4-tuples (x,t) there is a new set of commutation relations.
