Omega and One

The symbol: w+1. This is the smallest ordinal number after "omega". Informally we can think of this as infinity plus one. One formulation of ordinals is to treat them as sets of all smaller ordinals. In order to say omega and one is "larger" than "omega" we define largeness to mean that one ordinal is larger than another if the smaller ordinal is included in the set of the larger. The set w+1 would be {w,0,1,2,3,...}. It would be composed of all the non-negative integers plus omega. Thus w+1 by this definition is larger. However, since the cardinality of every ordinal is represented by the cardinality of it's set, we can also show that in a sense w = w+1, since w={0,1,2,3,...} and w+1={w,0,1,2,...} we can pair off arguments as: {(0,w),(1,0),(2,1),(3,2),...}, which shows both sets have the same number of elements, even though w+1 includes one more. Confused? Basically there is two ways to look at comparison of infinities: the cardinal view and the ordinal view. By the ordinal view, omega and one is greater, by the cardinal view omega and omega plus one are the same thing. Cardinals don't play a large role in googology, but the countable ordinals do. So for our purposes the distinction between w and w+1 is important. (I copied this off a google site)

guy: yo I have omega and one pencils
guy 2: how the (AUUUUGGGGHHH) do you have omega and one

by SauceQuest31 December 29, 2022

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one-hit

See: Millennial

Ever notice how these one-hitters are so shielded these days?

by SomeGuyWhoThinksHeKnowsItAll November 14, 2018

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One in the Quiver

When you have one nut left to bust, like having one arrow in the quiver

Person 1: "Broooo, me and my gf had some rough anal sex! She left me with One in the Quiver!!!!"
Person 2: "That's intense!"
Person 1: "I know! If I had cummed one more time, I would have been done for!"

by Tr1d3nt August 3, 2017

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