Cantor Function Puns

Why is the CDF of cantor function called the 'Devil's staircase' ? What is devilish about it ?

So I am using currently a cantor function, ((x + y)*(x + y + 1) + x)/2, to get a unique value for sets of coordinates so that I can check if I have visited the coordinates or not. I am just curious what the worst case time complexity of this function would be assuming im given the number of rows and columns. It would be O(n) correct? Or would it be O(n^2)?

For each r in (0, 1), let f_r: [0, 1] -> R be the middle-r Cantor function. Does the sequence of iterates f_r, f_r^(2), f_r^(3), ... converge pointwise?

If it exists, can we identify the limit function? In particular I am interested if it is discontinuous.

I was wondering if there’s a formula for the inverse of Cantor bijective mapping function for n-tuple inputs, I know there’s an inverse for n=2 and that the Cantor function is invertible for any number of inputs. What do you think? Is there such an inverse function?

The Cantor Pairing Function maps two natural numbers to a unique natural number. Does this function also work for positive reals (excluding 0)?

Why is the cantor set uncountable, it makes no sense, and on top of that, that devil's staircase nonsense is driving me insane. I just want to pretend it's countable, just a little bit longer, this is straight out of HP Lovecraft.

Also posted this to r/maths: First 4 paragraphs (including this one) are essentially background information explaining what I (believe to) know and understand and my lead up to my question.

First want to clarify I’m a second year theoretical physicist, so the maths I’ve been learning at university isn’t very rigorous, and my interest in this topic is a result of just being interested in maths so my terminology etc may be incorrect, I will find it helpful if I am corrected so please do! My use of the word cardinality is probably a bit dodgy at some points as I’ve learnt it through context.

I’ve known for a while now that there are different infinities and some are larger than others, such as aleph 0, which is the cardinality of the natural numbers and integers and is countable. I also know of aleph 1 which is the cardinality of the real numbers and aleph 2 which is the cardinality of the set of real functions. I also know there is no largest infinity, Cantor’s theorem allowing you to find an infinity essentially of a cardinality of ‘1 more1 the same way we have aleph 2 having a cardinality of ‘1 more’ than aleph 1, that’s the best way I can put it as my terminology or notation isn’t good enough to describe it rigorously but I do understand the concept.

I am also aware that there is no cardinality between aleph n and aleph n + 1, and that there is no set of cardinalities, and that it would technically be a class, and a class that isn’t a set has no cardinality, but is ‘infinitely large’ (I think?).

My question is whether the amount of infinite cardinalities, e.g. aleph 0, … aleph n, … is countable.

I am predicting it to be countable as I see a link with the natural numbers as there is no cardinality between aleph n and n + 1 as we are effectively ‘increasing each cardinality by 1’, and the ‘largest infinity’ is the same as the ‘largest natural number’ in the sense where if you think of the largest one, you can always find a larger one by simply adding 1, or in the case of the infinities, you can take 2^|aleph_n| to get aleph_n+1.

Sorry for the really long post for literally just 1 short question but it’s an incredible topic that is difficult to grasp intuitively.

Hello, I’m a math first year student and recently learned about Cantor’s theorem regarding the comparison of cardinalities between infinite sets.

I have had a lot of difficulty though with rationalizing a good intuition about some of the deductions derived from it, specially ones such as the cardinalities of the natural numbers and rational numbers being the same, or of the natural numbers having a smaller cardinality than all real numbers in the interval of 0 and 1 that has the same cardinality as the real numbers (I have been able to understand the theory behind those but even so it still feels very counter intuitive to me).

So in trying to get a better intuition for it I though about a lot of examples that would derive from the theorem and it’s implications and ended up thinking of a counter example to one of the implications from Cantor’s theorem that I wasn’t able to figure out why it would be wrong.

The counter example I had thought of would be a bijective function that would link all natural numbers plus some rational numbers to all real numbers in the interval between 0 and 1.

The general logic of the function would be the following:

The input of the function would be a set spanning all natural numbers as well as a “few” rational numbers (I will better specify which are those rational numbers later)

So for this function, let’s call it F, we would have a certain value F(x) if x € N.

This value would be calculated by assigning each natural number (ex: 1,2,3,4,5) to a respective decimal between 0 and 1 (ex: 0.1, 0.2, 0.3, 0.4, 0.5) following the intuitive rule that you might have noticed between both examples.

If x is a natural number divisible by 10 though, such as 10 or 20, we would have a problem using the simple rule from above as 10 would lead to 0.10 and 20 would lead to 0.20, both of which can be simplified to 0.1 and 0.2. Both of these values had already been obtained from x=1 and x=2, which would mean the function is not injective. We can dodge this problem though by instead assigning the value of 10 to what would be the next decimal value(ex: 0.11), so we would be able to continue with 11>0.12, 12>0.13, 13>0.14 and so on( the “>” sign was used to mean leads to rather than it’s bigger than in this occasion).

Now following this rule we should have a function that leads all natural numbers to all decimal numbers between 0 and 1 that have a similar structure to how natural numbers are written.

There is still a problem t

Hello all.

I'm still relatively new to modern (just under a year) and I have settled on a Grixis Shadow midrange deck helmed by [[Lurrus of the Dream-Den]]. Aside from a playset of [[Ragavan, Nimble Pilferer]], I felt like it's a pretty standard list. However, I have noticed differences between mine and the ones I see kicking around (I don't have a digital deck list to share for contrast). I've been looking through the lists and I have noticed the following inclusions/exclusions that I don't understand.

• [[Tourach, Dread Cantor]] is featured. What matches would Tourach be a valuable addition? He seems to be a good beater, but I already have [[Death's Shadow]], [[Scourge of the Skyclaves]], and [[Kroxa, Titan of Deaths Hunger]]. Between [[Thoughtseize]], [[Inquisition of Kozilek]], and [[Kolaghan's Command]] I have plenty of discard. What shortcoming does Tourach compensate for?

• [[Damping Sphere]] is absent. This seems like an all-star silver bullet vs Tron, Amulet Titan, Storm, and decent against Cascade. Sphere + threat seems like a solid tempo blowout in those matchups. Has this been cut for [[Chalice of the Void]], [[Void Mirror]], and/or [[Alpine Moon]]? Why should I prefer one over the other?

• [[Dress Down]] seems fun, but it's not intuitive to play. IDK how many to run in the main deck, how many to have in the sideboard, and what matchups to bring it in. It gets stuck in my hand more often than not.

• [[Stubborn Denial]] and [[Temur Battle Rage]] are seemingly all but gone. I thought these were ubiquitous with Death's Shadow. What changed?

I know this seems like a stupid question, but a part of me feels like I fundementally misunderstand how this deck functions--internally and in context of the larger meta. What I am missing about these cards? Please be polite, I am genuinely confused about the presence/absence of these cards.

Do your worst!

It really does, I swear!

For context I'm a Refuse Driver (Garbage man) & today I was on food waste. After I'd tipped I was checking the wagon for any defects when I spotted a lone pea balanced on the lifts.

I said "hey look, an escaPEA"

No one near me but it didn't half make me laugh for a good hour or so!

Edit: I can't believe how much this has blown up. Thank you everyone I've had a blast reading through the replies 😂

I'm surprised it hasn't decade.

They’re on standbi

Buenosdillas

Pilot on me!!

Dad jokes are supposed to be jokes you can tell a kid and they will understand it and find it funny.

This sub is mostly just NSFW puns now.

If it needs a NSFW tag it's not a dad joke. There should just be a NSFW puns subreddit for that.

Edit* I'm not replying any longer and turning off notifications but to all those that say "no one cares", there sure are a lot of you arguing about it. Maybe I'm wrong but you people don't need to be rude about it. If you really don't care, don't comment.

There are infinite sets whos cardinalities are different (e.g. countable sets vs uncountable sets) but what is the logic for sorting them by size?

For example, we would rank the cardinality of the real numbers as being larger than the rationals. But, what is the rule or logic that results in this ordering?

Don't get me wrong, this ordering makes sense, but I struggle to think of the formal rule or rules that underpin this ordering.

For example (again), it isn't sufficient that the reals contain numbers that the rationals do not, or that the rationals are a strict subset of the reals as there are countably infinite sets that contain numbers other countably infinite sets do not, or are strict subsets of each other, yet they all have the same cardinality.

When I got home, they were still there.

What did 0 say to 8 ?

" Nice Belt "

So What did 3 say to 8 ?

" Hey, you two stop making out "

I won't be doing that today!

You take away their little brooms

This morning, my 4 year old daughter.

Daughter: I'm hungry

Me: nerves building, smile widening

Me: Hi hungry, I'm dad.

She had no idea what was going on but I finally did it.

Thank you all for listening.

There hasn't been a post all year!

[Removed]

First 4 paragraphs (including this one) are essentially background information explaining what I (believe to) know and understand and my lead up to my question.

First want to clarify I’m a second year theoretical physicist, so the maths I’ve been learning at university isn’t very rigorous, and my interest in this topic is a result of just being interested in maths so my terminology etc may be incorrect, I will find it helpful if I am corrected so please do! My use of the word cardinality is probably a bit dodgy at some points as I’ve learnt it through context.

I’ve known for a while now that there are different infinities and some are larger than others, such as aleph 0, which is the cardinality of the natural numbers and integers and is countable. I also know of aleph 1 which is the cardinality of the real numbers and aleph 2 which is the cardinality of the set of real functions. I also know there is no largest infinity, Cantor’s theorem allowing you to find an infinity essentially of a cardinality of ‘1 more1 the same way we have aleph 2 having a cardinality of ‘1 more’ than aleph 1, that’s the best way I can put it as my terminology or notation isn’t good enough to describe it rigorously but I do understand the concept.

I am also aware that there is no cardinality between aleph n and aleph n + 1, and that there is no set of cardinalities, and that it would technically be a class, and a class that isn’t a set has no cardinality, but is ‘infinitely large’ (I think?).

My question is whether the amount of infinite cardinalities, e.g. aleph 0, … aleph n, … is countable.

I am predicting it to be countable as I see a link with the natural numbers as there is no cardinality between aleph n and n + 1 as we are effectively ‘increasing each cardinality by 1’, and the ‘largest infinity’ is the same as the ‘largest natural number’ in the sense where if you think of the largest one, you can always find a larger one by simply adding 1, or in the case of the infinities, you can take 2^|aleph_n| to get aleph_n+1.

Sorry for the really long post for literally just 1 short question but it’s an incredible topic that is difficult to grasp intuitively.