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Other symbols i have seen used for is defined to be equal to are three horizontal lines instead of two, and $=$ with either a triangle or def written directly above it Can someone give me a detailed breakdown as to the differences in their meanings, their uses and the situations for which each should be used? I have seen variants of these used by people who predate widespread knowledge of computer programming

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It would be interesting to know the earliest uses of a special symbol for this (and what symbols were chosen) It seems like perpendicular and normal would not have a nice meaning whereas orthogonal would as it is defined in terms of the dot product I have encountered this when referencing subsets and vector subspaces

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Is ⊊ a sort of ≤ or &lt.

The curly versions of the less than and greater than signs are commonly used to denote some other ordering than the one that we are usually talking about For instance there is a partial ordering on the symmetric matrices, where a≼b a ≼ b if and only if b−a b a is a nonnegative definite matrix We write ≼ ≼ instead of ≤ ≤ to avoid confusion with the ordering that we use more. Whats the meaning of this symbol

Its a three dot symbol ∴ i read a book, im could not find any definition of this symbol This is about continuum property of the natural numbers and the archimed. What exactly does $\\ll$ mean

I am familiar that this symbol means much less than.but what exactly does much less than mean

(or the corollary, $\\gg$) on wikipedia, the example they use i. The meaning of various equality symbols ask question asked 10 years, 7 months ago modified 9 years, 7 months ago Does it mean either less than or greater than In other words, not equal

I am trying to understand a book that says th. Since your professor was referring to engineering students, then it's likely they were referring to the identity symbol, which is used in an expression to mean the left and right hand sides are true for all values So $\cos^2\theta +\sin^2\theta \equiv 1 $ since it's true for all $\theta$ whereas $\cos\theta = 1$ since it's true only for some. The interplay of meaning and axiomatic machine mathematics, captured by the difference between $\models$ and $\vdash$, is a subtle and interesting thing.