Hi, I have a question about the bending of spacetime and its proportion and relation to the mass which causes the bending; and also how the bent space would interact with other objects as they come closer.
I'm gonna ask a more detailed question with some possible problems I would like to...
What math is useful for distinguishing and classifying things based only on relations they satisfy?
For example the relation ##R_1 = \{(a,b), (b,a)\}## isn't useful for distinguishing "a" from "b" while the relation ##R_2 = \{(a,b), (c,b) \}## lets us distinguish "b" by the description "The...
Homework Statement
Prove or disprove: Every translation is a product of two non-involutory rotations.
Homework Equations
The Attempt at a Solution :[/B]
I am not sure if I got the right proof for the special situation: A translation is the product of two reflections with parallel reflections...
Homework Statement
Homework Equations
I don't think there are any in this case
The Attempt at a Solution
I know that in order to prove R is an equivalence relation, I'd have to show that it is Reflexive, Symmetric, and Transitive. I'm not sure why, but I'm finding this a bit difficult in...
The definition of these relations as given in my textbook are :
(1):- Reflexive :- A relation ##R : A \to A## is called reflexive if ##(a, a) \in R, \color{red}{\forall} a \in A##
(2):- Symmetric :- A relation ##R : A \to A## is called symmetric if ##(a_1, a_2) \in R \implies (a_2, a_1) \in R...
Homework Statement
My task is to find out what is the lowest # of elements a poset can have with the following characteristics. If such a set exists I should show it and if it doesn't I must prove it.
1) has infimum of all its subsets, but there is a subset with no supremum
2) has two maximal...
I'm coming from a physics background, but find pure mathematics extremely interesting, so have decided to try and gain a more fundamental understanding of the subject. I've recently been reading up on relations and how one can define them as sets of ordered pairs. I am particularly interested in...
Apologies if this is in the wrong forum, but I chose to post here as the question pertains to equivalence relations and classes.
Sorry if it's such a trivial question, but what is the mathematical difference between equivalence and equality? My understanding is the following, but I'm a little...
Question: Find the equivalence classes and the number of equivalence classes of the following relations.
A is the set of all possible strings of 3 or 4 letters in alphabet {A, B, C, D}, and (x, y) ∈ R if and only if x and y have the same first letter and the same third letter.
My attempted...