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Apr
3
comment Finding the curvature of a line.
Not every curve can be aligned with a circle. Unless what you're really asking is "given the width/height of a circular arc, how can I determine how big the circle it's from is?".
Apr
2
comment Why is the construction of the real numbers important?
@industry7 That would certainly be another approach to motivating the concept of a real number. I chose my "if you needed a square root of two, you'd just pick an approximation" story because it's purely arithmetical (even if I chose to illustrate it with geometry). We just seem to be using the word "obvious" in different ways.
Apr
2
comment Why is the construction of the real numbers important?
@AsafKaragila If rationals are just equivalence classes, how do you justify their relation to the real world? How do you justify that chopping something into three pieces gives $1/3$ of what you originally have? Also, you then have to simply define the operations somewhat arbitrarily, when deep down you secretly know that those operations can be proven (informally, but still convincingly) to be correct. This dissonance between the formalization and your intuition means that the formalization isn't really useful, and rationals are pretty much just fundamental objects.
Apr
2
comment Why is the construction of the real numbers important?
@user21820 I explicitly constructed such an oracle in the post.
Apr
2
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Apr
2
revised Why is the construction of the real numbers important?
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Apr
1
revised Why is the construction of the real numbers important?
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Apr
1
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Apr
1
revised Why is the construction of the real numbers important?
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Apr
1
answered Why is the construction of the real numbers important?
Apr
1
revised Duplicated Number Perfect Squares
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Apr
1
revised Duplicated Number Perfect Squares
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Apr
1
answered Duplicated Number Perfect Squares
Mar
31
comment Description of $\mathbb Z/p^2\mathbb Z$ as an extension of $\mathbb Z/p\mathbb Z$
@hardmath Oh, right. That's what I meant.
Mar
31
asked Description of $\mathbb Z/p^2\mathbb Z$ as an extension of $\mathbb Z/p\mathbb Z$
Mar
31
comment Is Proof By Induction Necessary?
This is a duplicate of [this question], to the point that the question asker almost (possibly unintentionally) quoted that question verbatim.
Mar
29
comment What is abstraction of direction in considering vectors such as used in Engineering & Physics?
The direction of a vector is just the one-dimensional subspace that it generates.
Mar
29
awarded  Nice Question
Mar
29
revised A conjecture on uniform convergence of functions with a compact metric space
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Mar
29
answered Proving that $\Omega$ is bounded.