>>10919440Regular infinity is vested with freedom to do its algebraic operations in any order one wishes. The hat is an instruction not to do the additive absorptive operation. I'm not adding anything to regular infinity, I am simply telling you how to use the innate freedom to simplify or not to simplify.
What have added is an axiom that expression (inf-hat - B) have a certain ordering.
>What are you trying to accomplish here exactly?I'm trying to get about $600k after taxes from Clay Institute. If people reject the ordered field definition of R and use the cut-in-a-line definition I have presented because it is better and contains a subset which has everything in it given by the ordered field definition, then I will be happy to have created a new system of the world.
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Job 38
The Lord Speaks
38 Then the Lord spoke to Job out of the storm. He said:
2
“Who is this that obscures my plans
with words without knowledge?
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Brace yourself like a man;
I will question you,
and you shall answer me.
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“Where were you when I laid the earth’s foundation?
Tell me, if you understand.
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Who marked off its dimensions? Surely you know!
Who stretched a measuring line across it?
