😥
Flag: | Colombia |
Registered: | July 25, 2021 |
Last post: | December 30, 2024 at 5:54 PM |
Posts: | 8848 |
This is not a prediction thread, this is who do you want to see win today.
Personally i want both korean teams to succeed. Its gonna be depressing in this site if drx lose. Also i love xeta, his team had a massive glow up and i wanna see them do damage to bigger teams
the theorem is meta, it works in one map, and now works in all maps
sorry mr cresp, im not that advanced, yet
It is with utmost discernment that I present the notion that certain propositions, positioned amidst the tapestry of human understanding, are irrefutably beyond the confines of proof, owing not to their inherent enigmatic nature, but rather due to their intrinsic falsehood. These propositions, draped in a veneer of allure, masquerade as subjects worthy of profound inquiry, yet remain resolutely untethered from the realm of truth.
In this intricate dance of intellectual discourse, we encounter propositions that, upon meticulous examination, reveal themselves to be at odds with the bedrock of veracity. Through the discerning lens of logical scrutiny and empirical scrutiny, their foundations crumble, their coherence dissipates, and their inherent falsehood is laid bare.
Thus, it is incumbent upon us to recognize that amidst the vast landscape of propositions, there exist those that, like elusive phantoms, seek to seduce our intellectual faculties. However, armed with the discerning light of reason, we uncover their intrinsic fallacy, rendering them impervious to the realm of proof, for their very essence is constructed upon a foundation of untruth.
Since you guys seem to be fans of the binomial theorem, I cooked up the proof using mathematical induction for you guys
Proof of the Binomial Theorem:
Step 1: Base Case
For n = 1, the binomial theorem states:
(x + y)^1 = C(1, 0) x^1 y^0 + C(1, 1) x^0 y^1
which simplifies to:
x + y = x + y
This confirms that the base case holds true.
Step 2: Inductive Hypothesis
Assume that the binomial theorem holds true for some positive integer k:
(x + y)^k = C(k, 0) x^k y^0 + C(k, 1) x^(k-1) y^1 + C(k, 2) x^(k-2) y^2 + ... + C(k, k-1) x^1 y^(k-1) + C(k, k) x^0 y^k
Step 3: Inductive Step
We need to prove that the binomial theorem also holds true for k + 1. So, let's consider (x + y)^(k+1):
(x + y)^(k+1) = (x + y) * (x + y)^k
Using the distributive property, we can expand this as:
(x + y)^(k+1) = (x + y) (C(k, 0) x^k y^0 + C(k, 1) x^(k-1) y^1 + C(k, 2) x^(k-2) y^2 + ... + C(k, k-1) x^1 y^(k-1) + C(k, k) x^0 * y^k)
Expanding further and simplifying, we get:
(x + y)^(k+1) = C(k, 0) x^(k+1) y^0 + C(k, 1) x^k y^1 + C(k, 2) x^(k-1) y^2 + ... + C(k, k-1) x^2 y^(k-1) + C(k, k) x^1 y^k
Using the binomial coefficient identity C(n, r) + C(n, r+1) = C(n+1, r+1), we can simplify the expression further:
(x + y)^(k+1) = (x + y)^k + C(k, 0) x^k y^1 + C(k, 1) x^(k-1) y^2 + C(k, 2) x^(k-2) y^3 + ... + C(k, k-1) x^0 y^k + C(k, k) x^0 y^(k+1)
This can be rewritten as:
(x + y)^(k+1) = (x + y)^k + [C(k, 0) x^k y^1 + C(k, 1) x^(k-1) y^2 + C(k, 2) x^(k-2) y^3 + ... + C(k, k-1) x^0 y^k] + C(k, k) x^0 y^(k+1)
Notice that the term in the brackets matches the binomial theorem for k, so we can rewrite it as (x + y)^k. This simplifies the expression to:
(x + y)^(k+1) = (x + y)^k + (x + y) C(k, k) x^0 * y^(k+1)
Simplifying further, we have:
(x + y)^(k+1) = (x + y)^k + C(k+1, k+1) x^0 y^(k+1)
Since C(k+1, k+1) = 1, the expression becomes:
(x + y)^(k+1) = (x + y)^k + x^0 * y^(k+1)
This confirms that the binomial theorem holds true for k + 1.
Step 4: Conclusion
Since the base case holds true, and assuming that the theorem holds for k implies it holds for k + 1, we can conclude that the binomial theorem holds true for all positive integers.
Here is the link to the Pythagorean Theorem proof if you want to see more
im so sorry i didnt want to stay up till 6 am watching the games 😭
I didn't watch either Chinese game last night, it was just too late for me. My plan waking up was to enter vlr with spoilers hidden and search the vods. Maybe a Chinese team might have gotten upset and wanted to keep it a surprise, but the first thing I see upon entering vlr is that edg is playing against t1. Even with spoilers hidden that shit spoiled the upset 😭
Can you vlr devs please make it so upcoming matches get hidden with spoilers hidden feature? thanks
They make miracles happen, and when its needed the most
EZ4ENCE ENCE ENCE
Dens putted upperbelt
Putted upperbelt
Minorist majorii
Haastaa legendaarisii
Nyt isos liigas, niin ku Rosbergi
Suomalaist strättii maailmanluokan kaliberil
Kaks lasii maitoo ja yks lasi piimää
Ence kylvää ja ence siittää
Natun paljusta kansi avataan
Pojat on tulos, torilla tavataan
EZ4ENCE ENCE ENCE
Dens putted upperbelt
Putted upperbelt
EZ4ENCE ENCE ENCE
Dens putted upperbelt
Putted upperbelt
Allu on valmiina myllyttään
Vihut valmiina hyllyttään
Piti mennä A, mut mentiinki B
Nimikkotaktiikka aleksib
Nuori osuja sergej jakaa
Hiustyylei vanhaan tapaan
Xseven sitel lukottaa
Haastiksis mikin pudottaa
Aeriel shifti pohjas (Lento) kentil
Mut ekan saitil pelikentil
Kynärikansa tietää ketkä on äijii
Ence pistää ykösellä päihin
EZ4ENCE ENCE ENCE
Dens putted upperbelt
Putted upperbelt
EZ4ENCE ENCE ENCE
Dens putted upperbelt
Putted upperbelt
EZ4ENCE ENCE ENCE
Dens putted upperbelt
Putted upperbelt
EZ4ENCE ENCE ENCE
Dens putted upperbelt
Putted upperbelt
Bro fnatic lost to sentinels who lost to bbg. You guys are screwed
Lets be honest, t1 is so fucking good. This team is going to playoffs one way or snother 100%
Who knows, maybe they fixed some critical shit
They should just give raze an actual nuke lol
They got xeta, of course they are gonna be good
Its sad. But i believe they can defeat edg in the lowers pretty easily
If you want i can laugh, but it wont be free
Why were you spamming for both teams? 🤨
Took a fight against a judge close range and won lolz
Ok give me a second and ill message him directly to stop whiffing
There are no good matchups really. In reality they just gotta beat everyone to win
Hear me out, maybe , just maybe
Bottsi 🫵🤡
i feel they might pull an upset
Thanks for the deep analysis mr supernova
Screwface is the best player in the world
Imagine him in a fist fight. The opponent leaves untouched
Their gameplay is just way too clean what. Its like they complete threw the concept of lan nerves out of the window,and have decided to play valodant to perfection
Omg😱
However you got to thqt conclusion?🧐
Wait what if we reply to him with only emotes
Dont think that stat tells the whole story
They'll be good competition to chinese teams