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Just a layman and slow learner. Thank you for your enlightenment and patience, and for giving me the best memory in my life.


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comment In composition of two mappings, can the outer mapping access the arguments of the inner mapping?
Thanks. The domain of $f$ is the union of all finite-length real sequences. Does my notation $f: \cup_{i \in \mathbb N} \mathbb R^n \to \mathbb R$ in the post make sense now? $\cup_{i \in \mathbb N} \mathbb R^n$ is a disjoint union, because $\mathbb R^n$ is the set of all length-$n$ real sequences.
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reviewed Reject suggested edit on In composition of two mappings, can the outer mapping access the arguments of the inner mapping?
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revised In composition of two mappings, can the outer mapping access the arguments of the inner mapping?
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asked In composition of two mappings, can the outer mapping access the arguments of the inner mapping?
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revised Is a set of some $m \times n$ matrices a relation?
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comment Is a set of some $m \times n$ matrices a relation?
I am now ignoring the operations on the matrices and therefore any algebraic structure on the set of some matrices, just think a n by m matrix as a n by m array please. @whacka
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comment Is a set of some $m \times n$ matrices a relation?
@whacka: See the first line i just updated in my post. So what is a set of matrices, something more sophisiticated than a nm-ary relation on $\mathbb R$? Thinking it as a nm-ary relation on $\mathbb R$, will lose the dimension and size of the matrices.
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revised Is a set of some $m \times n$ matrices a relation?
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comment Is a set of some $m \times n$ matrices a relation?
@whacka: The question in my post is: Is a set of some n×m real matrices a relation or something more sophisicated? I haven't put any operation on the set of matrices yet, and the set can consist of any matrices or not.
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comment Is a set of some $m \times n$ matrices a relation?
@whacka: $A$ and $B$ are two arbitrary sets. see the definition of a relation.
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comment Is a set of some $m \times n$ matrices a relation?
@ShawnO'Hare: The question in my post is: Is a set of some n×m real matric a relation or something more sophisicated?
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revised Is a set of some $m \times n$ matrices a relation?
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comment Is a set of some $m \times n$ matrices a relation?
No, because from $\mathbb R^{nm}$, you can't tell it is two dimensional. A vector and a matrix are never the same.
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revised Is a set of some $m \times n$ matrices a relation?
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