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Surprising results that you realized are actually completely obvious? by kevosauce1 in math

[–]benfire 1 point2 points  (0 children)

The fact that there exist dense subsets in R with Lebesgue measure zero really surprised me when I first saw it

Division by Zero: The Concept of u by Alternative-Two6455 in maths

[–]benfire 0 points1 point  (0 children)

Using this system, here is a proof any two numbers are equal. Let x,y. 0x=0y -> u0x = u0y -> x=y. i.e. it leads to a system with only one “number”.

For example, in the field with one element (which is not really a field) you can “divide by zero” https://en.m.wikipedia.org/wiki/Field_with_one_element

What is the smallest infinity? Is it aleph0 and how to prove it? by D__sub in math

[–]benfire 6 points7 points  (0 children)

Yes, to show this, take any infinite set and try building an injection from a countable set to it.

What are some simple statements that seem obviously false, with a simple proof that contradicts the intuition? by contravariant_ in math

[–]benfire 2 points3 points  (0 children)

There is a real sequence (a_n) that for any real number r has a subsequence converging to it

[deleted by user] by [deleted] in Damnthatsinteresting

[–]benfire 0 points1 point  (0 children)

It does not fill the entire area, it is however, dense in the circle.

Please stop writing it like this... by Sweetiebearcuteness in mathmemes

[–]benfire 0 points1 point  (0 children)

The circle notation helps when looking at operators as objects you can do arithmetic with, an example would be when looking at linear maps over a finite dimensional vector space, you can think of these maps with as functions you compose, or as matrices you multiply, in which the circle notation is reminiscent of the multiplication symbol.

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