Surreal Number Puns

College has always had this daunting presence to me, like a huge wall I’d never get over no matter how long I climbed. I was constantly feeling overwhelmed and burnt out by the sheer amount of effort and time it would take to complete a degree. Still, no matter the pace, I kept working toward the finish line, mostly because I had no choice but to keep going. I’d forgotten why I was even doing it for a while and all passion toward my field of study has since drifted away.

Now, nearing the end of my “junior” year I finally see the light at the end of the tunnel. I will graduate with a bachelor’s degree after just TEN more classes. They’ll be the hardest and most advanced coursework I’ll come across but knowing that the end actually exists and is within my grasp is so relieving.

The anticipation and excitement of the end is giving me the drive to once again keep pushing forward. I can’t wait to complete my degree and move on with life and everything else it has to offer.

Much love to anyone who feels overwhelmed in the same way I was for so long. If you can, keep pushing and keep working because it adds up! It feels incredible to know your hard work is paying off.

I just finished A Little Life.

Sometimes, it’s almost like Jude’s pain seeps through the pages. But at the same time, this does not come off as excessive or sensational – it just is. This novel drove me mad and I hated reading it, at times. I don’t think I will read it again, frankly. But giving credit where it’s due - reading A Little Life was the most immersive experience I have ever had while reading a book.

I found the rulings for Infinity Elemental to be a little bit disappointing, considering some of the stuff you can do with surreal numbers and infinite ordinals. I barely understand the set theory stuff myself, but essentially, surreal numbers allow you to derive meaningful answers to questions like, "What is ∞ + 1"?

If we apply some of these constructions to a game with Infinity Elemental, we can have some fun.

Here's how things would go normally:

Let's say I attack with Infinity Elemental. I play Azorius Charm on it, temporarily giving it lifelink. You chump block. My life total is now ∞.
Let's say the same thing happens again on the next turn. I'm now at ∞.
Now say you swing for 4. I'm at ∞.
Now say you play Revenge and halve my life total. I'm at ∞.
Now say you swing at me with two infinity elementals. They wouldn't affect my life total, because apparently infinite power isn't enough to deal infinite damage.
But I decide to block one with my elemental.
5 - ∞ < 0, so they would trade. But I've got a trick up my sleeve. I play About Face on my blocker, transforming it into a 5/∞. My blocker would eat your attacker, because like I said, infinite power isn't enough to deal infinite damage. But 5 power is enough to deal 5 damage.
However, I've also got a Giant Growth, so I play that. My blocker is now an 8/∞. This was a waste of mana.
My blocker eats your attacker and your other attacker takes me from ∞ to ∞.

Now let's imagine this with surreal numbers.

Let's say I attack with Infinity Elemental. I play Azorius Charm on it, temporarily giving it lifelink. You chump block. My life total is now ∞ + 20.
Let's say the same thing happens again on the next turn. I'm now at 2∞ + 20.
Now say you swing for 4. I'm at 2∞ + 16.
Now say you play Revenge and halve my life total. I'm at ∞ + 8.
Now say you swing at me with two infinity elementals. That would put me at 8 - ∞, which is infinitely less than 0, meaning I would die. So I decide to block one with my elemental.
5 - ∞ < 0, so they would trade. But I've got a trick up my sleeve. I play About Face on my blocker, transforming it into a 5/∞. ∞ - ∞ = 0, and 5 - 5 = 0, so they would still trade.
However, I've also got a Giant Growth, so I play that. My blocker is now an 8/∞+3. This means it'll kill your blocker and be left with 3 health.
You play lightning bolt on it. It dies.
Your other elemental goes un

I've recently stumbled across Conway's Surreal Numbers. Every surreal number can be represented as a version of {L|R}, where L and R are sets of other surreal numbers, including the possibility of an empty set.

0 = {|}
1 = {0|} = {{|}|}   
-1 = {|0} = {|{|}}
2 = {1|} = {{0|}|} = {{{|}|}|}
1/2 = {0|1} = {{|}|{{|}|}}
1/4 = {0|1/2}
ω = {0,1,2,3,...|}
1/3 = {0, 1/4, 5/16, ... | 1/2, 3/8, 11/32, ...}
√(ω) = {1,2,4,...|ω,ω/2,ω/4,...}

Is there a way to represent √(-1), a.k.a. i, this way?

It can't be {0|0}, {-1|1}, nor any version of {-x|x}, because none of those have negatives (since negatives are defined as -x={-R|-L} for x={L|R}), but i does have a negative.

I'm aware of the existence of the so-called surcomplex numbers, but, if I understand correctly, they just use it as i≝√(-1), without defining a {L|R} form for it.

Edit: fixed typo
Edit2: improved formatting

I honestly do not know how to feel about most sources ranking us Number 1. I've been a Ravens fan for about 10 years now and that entire time we were straight up underdogs and usually never above top 5. Even in our playoff run where we won the Super Bowl, we were considered underdogs all the way. It truthfully feels so surreal seeing us Number 1 for the first time in my Ravens journey. It's like a dream. I don't know, but I like this feeling. Long live the Llama.

So, if I'm understanding this correctly, <1, 1/2, 1/4, 1/8, ... | 0> is a number smaller than 0 but bigger than every real number smaller than 0. The way I heard it explained was that these numbers fill in the gaps of the real numbers, but I'm having a hard time intuiting in my head what gaps exactly need to be filled.

How do you make sense of a number being less than another number but greater than every number less than it?

EDIT: I was told the number in the title is wrong. I'm aware of the issue, but I cannot fix it.

TL;DR at the bottom

I am reading Surreal Numbers by D. E. Knuth (it has been amazing so far) and I am currently on chapter 4 “Bad Numbers “(page 24). (You can read it here https://archive.org/details/SurrealNumbers/page/n16 ) The characters are trying to prove that if x<=y, y<=z then x<=z. They try to prove it by contradiction, so they suppose that there exists x,y,z such that x<=y, y<=z, x!<=z. This are called “bad numbers”.

They prove that if x,y,z are bad numbers, then y,z,xL are bad numbers too or zR,x,y are bad numbers too (so you could repeat this to get more and more sets of bad numbers). This new bad numbers are “simpler” because one of them was created on a previous day. So if the day in which a number was created is d(x), then d(x) + d(y) + d(z) = n, then the sum of the days of the new sets of bad numbers will be less than n. So if you keep creating bad numbers, the sum of their days will keep will be even less and so on. But that is impossible because d(x) + d(y) + d(z) can’t be less than 3. Therefore there can’t exist any bad numbers.

My problem is this: let’s say that we have a set of bad numbers called A. Using A we create a new ser of bad numbers called B. Using B we create a new ser of bad numbers called C. Lets say that the sum of the days of an X set of bad numbers is d(X). Since C is “simpler” than B, and B is “simpler” than A we know that d(C)<d(B) and f(B)<d(A). But how can we be sure that d(C)<d(A)? Isn’t this very similar to what we were trying to prove on the first place? (That if x<=y and y<=z then x<=z) so we can’t be sire that we will keep getting smaller and smaller results.

In fact in general, using the number of creation of the numbers seems odd to me, how do we even know that we can add d(x) and d(y)? What does “add” means? If d(x) is not a surreal number and is instead a natural number, then sure, this prove is ok and it makes sense, but it would have to use the help of the laws of natural numbers and it seemed to me like the whole point of the book was creating the surreal numbers from nothing, just relying on Conway”s rules. Even the story of the characters is similar to this concept, they escaped from their society and it’s rules to start from nothing.

Maybe this is in fact a mistake and the characters realize this later in the book and correct it, but I don’t know.

TL;DR In page 24 and 25 of Surreal Numbers ( https://archive.org/details/SurrealNumbers/page/n16 ), how can the

Is it possible to assign improper integrals over the reals a surreal value in a consistent way? Are there any papers available on this?

Note that I am not inquiring about formalizing integration over the surreal themselves, which I realize is still a somewhat open problem. Rather, I would like to identify an integral with a surreal such as

∫*0∞* x^2 dx = z ∈ Surreals

edit: I can never get LaTeX to work in this sub...

So I’m not on a committed day, as of yet, of nofap- I’ve been sexually active in the last month but couldn’t get myself to clinax to her without stimulating myself to cum on her so I think she thought I was just nervous but deep down(and trust me I know a lot of guys would fuck her silly) but I’ve always been one to want to make love od have sex with someone I’m more attracted to, until tonight.

I’ve been eying this girl for a few months. She comes into my work late at night and sometimes it’s when we’re too busy. Then tonight she came in my line, we smiled, exchanged a few words and that was it. For a few seconds I was thinking about how I will be at home tonight on the couch drinking ny beer thinking about that next chance to ask her, then thought of all the success stories on here and just had to go for it.

“I see you in here a lot, what’s your name?” ********” “Can I get your number?” “...sure :)”

She put it in my phone with her last initial included so we’re practically married at this point. No but for real, guys...the last chick told me I deserved to be happy and I really hope I can make this girl mine.