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butterfly-sapphire · 24 hours
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Robot genders where the number of parts represents your gender.
You have the odds and evens crowd.
The prime number crowd.
The mersenne primes.
The triangular number crowd.
Bots who have a non integer amount of parts.
So many genders. Bots often add or remove special parts on their wrists which are used to add or remove gender on the fly and is a large part of civilised society.
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Topological Spaces 4: Hausdorffness
In this post we will be discussing Hausdorffness. Loosely, Hausdorff spaces are ones where we can separate points using open sets. This will be our first example of a homeomorphism invariant and will allow us to prove that not all topological spaces are metrizable!
As always, this post will build on things from the previous posts in this series so it is a good idea to be familiar with them. Here is a link to the previous post.
Definition 4.1:
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Remark: The capital letter in Hausdorff comes from the fact it is a name. It is named after Felix Hausdorff who is one of the founders of topology and who included this condition in his original definition of a topological space!
We shall see our first example in the form of the following proposition.
Proposition 4.2:
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Examples 4.3:
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Remarks:
Since metric spaces are always Hausdorff, any space which is not Hausdorff cannot be metrizable. The two spaces above are examples of this.
There are spaces which are Hausdorff but are not metrizable. For an example, see the Golomb space
Proposition 4.4:
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Remark: This means that Hausdorff spaces are T₁.
Theorem 4.5:
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This is our first example of a homeomorphism invariant. As previously stated, we can use this to show that two spaces aren't homeomorphic if we know one is Hausdorff but the other isn't.
Hausdorffness is a very important property in topology. It is one of the required properties for a space to be a manifold (we'll see the full definition in a later post) which are objects of much interest!
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sleepy-bebby · 8 months
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mysharona1987 · 10 months
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Astronomy I-
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viejospellejos · 1 year
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theburninggalaxy · 8 months
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MATHS IS SUPER FUCKING QUEER FUCK THE WHOLE "IM GAY I CANT DO MATHS" BULLSHIT
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stranger-detective · 6 months
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Okay just saw a post where someone was talking about the correct order to do maths in an equation acronym and they said 'PEMDAS'??? I learned BEDMAS wtf is this shit
so
These are the only ones I've heard but idk there may be more
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mossy-woods · 1 year
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spirals in nature🌀🌀🌀🌀
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He's right tho
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Hey so you remember this thing that everyone on mathblr got excited about recently?
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This is the hat, and it's what's called an "aperiodic monotile". This means that no matter how you arrange copies of this tile, you can never get an arrangement that will repeat infinitely (think of it like the irrational numbers of tilings). This was big news in mathematics as while sets of more than one tiles have been found that are aperiodic (e.g: The Penrose Tiles), this was the first tile that's aperiodic by itself, hence "monotile". (There are some caveats to this but that's not important for understanding this post)
However.
If you look at images of the hat tiling, you may notice something.
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If you look at the tiles labled 1 and 2, you'll see that one's a reflected copy of the other. In fact, any infinite arrangement with hats requires you to you mix unreflected and reflected tiles. Which raises the question: is it possible to have an aperiodic monotile that doesn't need reflections?
Presenting the Spectre, A chiral aperiodic monotile.
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Using only translation and rotation, any arrangement of copies of this tile will never repeat.
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Mathematically speaking, this is really fucking cool.
The paper on it is still in preprint, but hopefully I won't need to retract this post. A copy of it can be found here and a post going into some more details of how the shape was discovered is here.
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sleepy-bebby · 2 years
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Easy way to find the centre of the board if it’s not an even number.
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incognitopolls · 2 months
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*This poll is asking what grade levels your school allowed to take calculus, not what grade you learned it. If you were homeschooled, though, you can put the grade in which you learned it.
For those with different grade/level structures, in the US 10th grade is typically age 15–16, 11th grade age 16–17, and 12th grade age 17–18.
We ask your questions so you don’t have to! Submit your questions to have them posted anonymously as polls.
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mysharona1987 · 2 years
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engineersthoughts · 7 months
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A GOAT doesn‘t care about physics. 🐐
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katiky-png · 7 months
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maths
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