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Good question but very difficult to answer. Before we find any evidence that supports continuity or discontinuity, we need to clarify what continuity means.

"Infinitely divisible" does not necessarily imply continuity. A series of rationals is infinitely divisible and was thought to be sufficient to represent all the points on a continuous line, but the discovery of incommensurables suggests that there are gaps between rationals.

Cantor's definition of continuous series are series that are Dedekindian and contain aleph_0 as a median class. But still, definitions like this do not preclude further discoveries of "gaps."

I think we need someone who is well-versed with Principia Mathematica to revise "the Principles," revisiting the same problems in the Principles by employing the tools and insights provided in Principia, using Principia not as a new dogma but as a stepping stone. He who can do this will have his name remembered for generations to come.

Good question but very difficult to answer. Before we find any evidence that supports continuity or discontinuity, we need to clarify what continuity means.

"Infinitely divisible" does not necessarily imply continuity. A series of rationals is infinitely divisible and was thought to be sufficient to represent all the points on a continuous line, but the discovery of incommensurables suggests that there are gaps between rationals.

Cantor's definition of continuous series are series that are Dedekindian and contain ℵ_0 as a median class, in virtue of which the series of reals are continuous. But still, definitions like this do not preclude further discoveries of "gaps."

I think we need someone who is well-versed with Principia Mathematica to revise "the Principles," revisiting the same problems in the Principles by employing the tools and insights provided in Principia, using Principia not as a new dogma but as a stepping stone. He who can do this will have his name remembered for generations to come.

Good question but very difficult to answer. Before we find any evidence that supports continuity or discontinuity, we need to clarify what continuity means.

"Infinitely divisible" does not necessarily imply continuity. The series of ratios is infinitely divisible and was thought to be sufficient to represent all the dots on a continuous line, but the discovery of incommensurables suggests that there are gaps between ratios.

Cantor's definition of continuous series are series that are Dedekindian and contain aleph_0 as a median class. But still, definitions like this do not preclude further discoveries of "holes."

I think we need someone who is well-versed with Principia Mathematica to revise "the Principles," revisiting the same problems in the Principles by employing the tools and insights provided in Principia, using Principia not as a new dogma but as a stepping stone. He who can do this will have his name remembered for generations to come.

Good question but very difficult to answer. Before we find any evidence that supports continuity or discontinuity, we need to clarify what continuity means.

"Infinitely divisible" does not necessarily imply continuity. A series of rationals is infinitely divisible and was thought to be sufficient to represent all the points on a continuous line, but the discovery of incommensurables suggests that there are gaps between rationals.

Cantor's definition of continuous series are series that are Dedekindian and contain aleph_0 as a median class. But still, definitions like this do not preclude further discoveries of "gaps."

I think we need someone who is well-versed with Principia Mathematica to revise "the Principles," revisiting the same problems in the Principles by employing the tools and insights provided in Principia, using Principia not as a new dogma but as a stepping stone. He who can do this will have his name remembered for generations to come.

Good question but very difficult to answer. Before we find any evidence that supports continuity or discontinuity, we need to clarify what continuity means.

"Infinitely divisible" does not necessarily imply continuity. The series of ratios is infinitely divisible and was thought to be sufficient to represent all the dots on a continuous line, but the discovery of incommensurables suggests that there are gaps between ratios.

Cantor's definition of continuous serious is one that is Dedekindian and contains aleph_0 as a median class. But still, definitions like this do not preclude further discoveries of "holes."

I think we need someone who is well-versed with Principia Mathematica to revise "the Principles," revisiting the same problems in the Principles by employing the tools and insights provided in Principia, using Principia not as a new dogma but as a stepping stone. He who can do this will have his name remembered for generations to come.

Good question but very difficult to answer. Before we find any evidence that supports continuity or discontinuity, we need to clarify what continuity means.

"Infinitely divisible" does not necessarily imply continuity. The series of ratios is infinitely divisible and was thought to be sufficient to represent all the dots on a continuous line, but the discovery of incommensurables suggests that there are gaps between ratios.

Cantor's definition of continuous series are series that are Dedekindian and contain aleph_0 as a median class. But still, definitions like this do not preclude further discoveries of "holes."

I think we need someone who is well-versed with Principia Mathematica to revise "the Principles," revisiting the same problems in the Principles by employing the tools and insights provided in Principia, using Principia not as a new dogma but as a stepping stone. He who can do this will have his name remembered for generations to come.