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what does ∇ (upside down triangle) symbol mean in this problem. Ask Question Asked 14 years, 2 months ago.
For a closer similarity "≃" might mean a triangle almost congruent but only ROUGHLY similar, such as two triangles 3/4/5 and 3.1/4.1/5.1 while "≅" means congruent. Real life triangles use approximations and have rounding errors. 3/4 does not equal 3.1/4.1 but could be rough approximations for something already constructed.
Here's a not too well-known instance of the use of $\varepsilon$ in mathematics: One somewhat well-known transformation for accelerating the convergence of a sequence is the Shanks transformation (after Daniel Shanks, who is probably more well-known for his number-theoretic contributions).
Writing {\displaystyle x\in A} x\in A means that "x is an element of A". Equivalent expressions are "x is a member of A", "x belongs to A", "x is in A" and "x lies in A". The expressions "A includes x" and "A contains x" are also used to mean set membership, however some authors use them to mean instead "x is a subset of A".
So, $↦$ is really just the math operator/binder $λ$, in disguise. Thus, one might just as well write $(x ↦ x^2)(3) = 3^2 = 9$ , denoting the function directly rather than through a level of indirection.
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 is that $1\ll 9999999999$ But my thought on that is that $10^{10^{10^{11}}}\ll 10^{10^{10^{11}}}+9999999999$, based on the same logic. But I am confused ...
$\begingroup$ I was aware of Pascal using :=, but not the others.I think it is possible that the language designers of that time where influenced by maths (as has happened a number of times), but := is so far the only easily typable symbol mentioned here, so it is perfectly reasonable to assume it stems from programming languages in the first place.
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$\begingroup$ @Brian M. Scott What does it mean when each subscript is non-numerical, and is exactly the same? I have an equation that has a value T (temperature in Kelvin), subscripted gamma. It's used several times each the same way, no variation, and all other equations in the same family simply use T, unsubscripted. What might that mean ...
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