IHOMO
Alternative spelling of IMHO, designed to fully appreciate the gayness of netiquette. Great for flamewars.
IHOMO by Mark2o98fuz November 27, 2007
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isomorphism
Abstract algebra: Take a group G, and a group H, with a group operation *. G is isomorphic to H if there exist a map f: G->H such that:
1: f is injective
2: f is surjective
3: f(a*b)=f(a)*f(b) for all a,b in G
If f satisfies these three properties, f is called an isomorphism.
1: f is injective
2: f is surjective
3: f(a*b)=f(a)*f(b) for all a,b in G
If f satisfies these three properties, f is called an isomorphism.
The map f: Z -> E given by f(a)=2a where Z is the integers and E is the even integers is an isomorphism.
Proof:
Showing injectivity
f(b)=f(a) => 2a=2b (from the given function) <=> a=b
Showing surjectivity
Suppose n is in E. n is an even integer hence n=2k for some integer k.
f(k)=2k=n, hence f is surjective.
Homomorphism:
f(a+b)=2(a+b)=2a+2b=f(a)+f(b)
Hence f is an isomorphism. Q. E. D.
Proof:
Showing injectivity
f(b)=f(a) => 2a=2b (from the given function) <=> a=b
Showing surjectivity
Suppose n is in E. n is an even integer hence n=2k for some integer k.
f(k)=2k=n, hence f is surjective.
Homomorphism:
f(a+b)=2(a+b)=2a+2b=f(a)+f(b)
Hence f is an isomorphism. Q. E. D.
isomorphism by qsqazxcvfrew March 29, 2018
Related Words
IHOMO • ihome • isomorphism • iFomo • Ihamod • ihmoyhy • iHomer • ihookedupwithnickyyknow • ihookedupwithsapphireyk • ihoop
ihome
A small, circular loudspeaker that can charge any electronics with a usb cable. It also has Bluetooth, and the quality of the music is excellent. I really recommend it, it has a good price, too.
ihome by HeavyMetalRocks January 6, 2015
IOMOS
Fuck everyone, Iomos!
Isomorphic JavaScript
A JavaScript application which can be executed in both a browser and a non-browser runtime. This was the first term used to describe this concept, but "Universal JavaScript" now has wider acceptance. Mathematicians and functional programmers will scoff at you if you use "isomorphic" to describe JavaScript, so save face by using "universal" instead.
Isomorphic JavaScript by chexxor March 30, 2017
ioMoVo
ioMoVo is the cloud storage system where you can enjoy the cloud ownership experience wherever your apps and data live. Being a subscription-based Software-as-a-Service (SaaS) solution, ioMoVo platform expands on typical cloud storage by giving users access to our proprietary Bring-Your-Own-Storage (BYOS) model, along with a comprehensive set of features that makes dealing with content much more effortless. Using intuitive asset movement and consolidation, AI-based search, and workflow automation, it provides a complete user experience in a single interface.
iFomo
A jealous obsession felt by the few who, when around their friends who all have iPhones, have a fear of missing out on the many advantageous entertainment methods an iPhone has to offer over 'ye olde mobiles'.
(Two friends sitting on the same couch playing 'Words with Friends'...whilst a third friend sits in between, only with his primitive 'button phone' to keep him entertained)
Friend 1 (iPhone): Bullshit, there's no way what you just sent is a word, you made that up!....(enters a reply word to Friend 2). Suck on this fgt!
Friend 2 (iPhone): Haha you idiot, you're guessing this shit as much as I am!
Friend 3 (Non-iPhone): -_- (wondering wtf is going on) ...man I got some serious iFomo.
Friend 1 (iPhone): Bullshit, there's no way what you just sent is a word, you made that up!....(enters a reply word to Friend 2). Suck on this fgt!
Friend 2 (iPhone): Haha you idiot, you're guessing this shit as much as I am!
Friend 3 (Non-iPhone): -_- (wondering wtf is going on) ...man I got some serious iFomo.