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:
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:
Examples 4.3:
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:
Remark: This means that Hausdorff spaces are T₁.
Theorem 4.5:
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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Pick an option at random :)
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Once you get to a certain level of advanced maths, you basically become a wizard.
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From the math Tumblr discord server:
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did you know they say calculus is the language of God. did you know they tried to hold math up to infinity like a candle to the void. did you know statisticians plunged into the vastness of random chance and picked out patterns and equations and eight hundred ways to tell you how big your inevitable errors are and how far off those guesses at errors might be. math haters I can't sit with you anymore. human innovation is cradled in these ancient, methodical, desperate attempts at understanding what we are not designed to understand
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why is this so funny to me
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“ok is this math really useful though what’s the point of it existing does it matter or is there no practical application” alright. if you write a poem does it matter? Is there an application? What if I killed you
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Grad school quote of the day:
“Lovely man. They shouldn't let him teach.”
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MATHS IS SUPER FUCKING QUEER FUCK THE WHOLE "IM GAY I CANT DO MATHS" BULLSHIT
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I just think math proofs should be formatted like green text
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Pick an option you think others won't pick.
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I didn't wanna derail the other post but I still wanna spread some love for my favourite subject...
Reblog if you've ever felt genuine joy or excitement from doing and/or thinking about math
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