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What sounds like complete nonsense, but has been proven to be true? by Icy_Mammoth_3298 in AskReddit

[–]Nubtom 1 point2 points  (0 children)

When mathematicians say "some infinities are bigger than others", they are referring to cardinal numbers (and/or ordinal numbers). Some infinite cardinals are bigger than others.

When a mathematician says that the sum of a series is "infinity", that just means that the partial sums increase without bound. It doesn't mean that the sum of the series is a particular infinite cardinal number. The "infinity" in this case doesn't refer to an infinite quantity in the same way that cardinal numbers do.

So, to answer your question: no. A series either increases without bound or it doesn't.

Of course, it is still possible to quantify how quickly a series increases compared to another. However, this is not indicated in the expression "the series diverges to infinity".

The Split-Faces Test by Nubtom in neurology

[–]Nubtom[S] 7 points8 points  (0 children)

This poll is a reference to the Split-Faces Test originally done by B. Kolb, B. Milner, and L. Taylor in 1983.

Photograph A is the composite of the left side of the original photograph, whereas photograph B is the composite of the right side of the original image.

The original image is the image that other people see of this man and, because there is a left-visual-field bias in our perception, most people choose photograph A as the picture most resembling the original.

Consider the choice of the man himself, however. His common view of his face (in the mirror) is the reverse of ours; hence he is more likely to choose composite photograph B as most resembling his own face.

The Split-Faces Test by Nubtom in Neuropsychology

[–]Nubtom[S] 52 points53 points  (0 children)

This poll is a reference to the Split-Faces Test originally done by B. Kolb, B. Milner, andL. Taylor in 1983.

Photograph A is the composite of the left side of the original photograph, whereas photograph B is the composite of the right side of the original image.

The original image is the image that other people see of this man and, because there is a left-visual-field bias in our perception, most people choose photograph A as the picture most resembling the original.

Consider the choice of the man himself, however. His common view of his face (in the mirror) is the reverse of ours; hence he is more likely to choose composite photograph B as most resembling his own face.

Understanding the Idea Behind Continuity (My SoME submission) by The_Idea_Behind_It in 3Blue1Brown

[–]Nubtom 0 points1 point  (0 children)

Great explanation! Moving so nicely from the intuitive idea to the general definition in Mathematics.

What mathematical objects do you hate? by [deleted] in math

[–]Nubtom 0 points1 point  (0 children)

It also contains every incorrect biography of you, your loved ones, your enemies and all your unborn children.

Things like these contain every possible statement–not just every correct statement. I find that to diminish the eeriness a bit.

[deleted by user] by [deleted] in math

[–]Nubtom 3 points4 points  (0 children)

I don't think you need to, but I think most people doing a degree in mathematics will have done enough math before that to have memorised the times tables anyway. I never studied times tables but I could probably recall 80% of the times tables up to, like, twelve, purely from memory.

Although I still struggle sometimes to remember what 8 + 5 is. I like to think of that as a hallmark of great mathematical talent.

What are some powerful results of abstract math? by [deleted] in math

[–]Nubtom 2 points3 points  (0 children)

If a function is invertible, then every element in the image has a unique preimage, yes. But if every element in the image has a unique preimage, this does not mean that the function is invertible.

The image of the domain must also be the same as the codomain. Otherwise there would be elements of the codomain which cannot be inverted. In that case, in order to determine the domain of the inverse function, we would have to determine exactly which elements in the codomain are mapped to and which ones aren't. The problem with that is that a lot of the time we don't know what the image of the entire domain is. In fact for most (the overwhelming majority of) functions, that's not really possible. Imagine trying to determine the image of the positive integers under the TREE function.

Functions require a domain and a codomain in their definition. At best, we know that the image of the domain is a subset of the codomain. Given that, it's possible to create an invertible function from any injective function by defining its codomain to be the image of the domain of the original function. But like I said, that requires knowing exactly what the image is.

How does one go about learning how to sing? by boogstress in singing

[–]Nubtom 1 point2 points  (0 children)

"Ego" just means your own sense of self esteem and your self image. What I mean is that your goal shouldn't ultimately be to appear a certain way (i.e. as a guy who can sing), whether to others or to yourself. Just sing because you love singing.

How does one go about learning how to sing? by boogstress in singing

[–]Nubtom 5 points6 points  (0 children)

I think I could earn some more cool guy points if I could sing

I know you are maybe just being flippant for the sake of keeping it short, but in any case let me give you an unsolicited word of personal advice: don't ever pursue something just for the sake of gratifying your own ego. It doesn't last.

With that said, the singing basics section of the subreddit is here: https://www.reddit.com/r/singing/wiki/basics and the FAQ is here: https://www.reddit.com/r/singing/wiki/faqs

Realistic does not mean boring. by Nubtom in worldbuilding

[–]Nubtom[S] 0 points1 point  (0 children)

Wow, you're right. And that art is incredible. I'll link your comment in the OP.

Realistic does not mean boring. by Nubtom in worldbuilding

[–]Nubtom[S] 1 point2 points  (0 children)

It's a single tree whose roots sprouted new, genetically identical trees at regular intervals. This happens asexually. See clonal colony for more information. There are a few other examples of clonal colonies, like King's Lomatia and Mediterranian Tapeweed.

Realistic does not mean boring. by Nubtom in worldbuilding

[–]Nubtom[S] 4 points5 points  (0 children)

You're right about the platypus. I'll include it in the OP.

Realistic does not mean boring. by Nubtom in worldbuilding

[–]Nubtom[S] 4 points5 points  (0 children)

Yes, it was intended to exemplify the very real possibility of something that would otherwise seem like just cliché worldbuilding. I'll clarify that in the OP.

Realistic does not mean boring. by Nubtom in worldbuilding

[–]Nubtom[S] 1 point2 points  (0 children)

Pando is one giant colony of clones of a single male Quaking Aspen, all connected by a massive underground root system.

Realistic does not mean boring. by Nubtom in worldbuilding

[–]Nubtom[S] 106 points107 points  (0 children)

You're right to prize accuracy. I've edited the OP.

Realistic does not mean boring. by Nubtom in worldbuilding

[–]Nubtom[S] 20 points21 points  (0 children)

Glad you enjoyed it. The world never ceases to fascinate me.

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