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  1. K

    Prove Set of all onto mappings from A->A is closed

    Still not very sure on how to start. BTW, is there anything rescuable from my first approach?
  2. K

    Prove Set of all onto mappings from A->A is closed

    Thanks. We need to show that ##fog## is onto or in other words fog = z = f(g(x)) =A? f: A-> A : f(a) = A g: A ->A: g(a) = A Is this correct?
  3. K

    Prove Set of all onto mappings from A->A is closed

    Homework Statement Prove that set of all onto mappings of A->A is closed under composition of mappings: Homework Equations Definition of onto and closure on sets. The Attempt at a Solution Say, ##f## and ##g## are onto mappings from A to A. Now, say I have a set S(A) = {all onto mappings of A...
  4. K

    Show that is not onto (##\frac{x}{x^2+1}##)

    Once, I have ##y(x^2+1) = x## what else can I do? ## y x^2 + y = x## divide all over x^2 wouldn't work.
  5. K

    Show that is not onto (##\frac{x}{x^2+1}##)

    The question says that A= R-{0} and B =R. Then, that f:A ->B and I need to show whether they 1-1 and whether they are onto. Prove. Thanks for the hint.
  6. K

    Show that is not onto (##\frac{x}{x^2+1}##)

    Homework Statement I need to show that $$\frac{x}{x^2+1}$$ is either onto or not. My domain is $$R-{0}$$ and range is $$R$$ Homework Equations I have learn to do this to show that a function is surjective y = $$\frac{x}{x^2+1}$$ and solve for x, but I am not sure how to proceed here. The...
  7. K

    Bohr-Sommerfeld Rule

    Homework Statement Imagine that force for is atom was ## F= - \frac{\beta}{r^4}##, rather than ##F=- \frac{ke^2}{r^2}##, and consider only circular orbits, it would remain true that ##L_n= n \hbar## a.) From Netwon's law find the relationship between ##T ##(Kinetic Energy) and ##V##, b.) Find...
  8. K

    Ambiguous GRE Question?

    Thank you, I understand now.
  9. K

    Ambiguous GRE Question?

    Homework Statement Title of pie chart: New Construction in Daisy Hill Subdivision Given a pie chart with sections: Currently Completed: 26% Currently Under Construction: 42% Approved, but Not Yet Started: 32% Question: When construction is completed in Daisy Hill Subdivision there'll...
  10. K

    Classical Relativity and the Speed of Light

    Homework Statement Let's assume that the classical ideas of space and time are correct, so that there could only be one frame, "ether", in which light traveled with same speed in all directions. Assume that the earth's speed relative to the ether frame is our orbital speed around the sun...
  11. K

    Relativity of Orientation & Origin

    Ok, thank you. I remember things better now. ## F_{net} = m*a ## ## F_x = m*g*sin(\theta)## ## F_{\mu} = \mu * F_N## ##F_{net}= F_x- F_{\mu}=m*a## ## a = g(sin(\theta) - \mu(cos(\theta)))## Finally, ## S(t)= (1/2)g(sin(\theta) - \mu(cos(\theta)))* t^2 ##
  12. K

    Relativity of Orientation & Origin

    Homework Statement At time t=0, a block is released from point O on the slope shown in the figure. The block accelerates down the slope, overcoming sliding friction. a.) Choose axes 0xy as shown, and solve the equation ##\Sigma F = m a## into its x and y components. Hence find the block's...
  13. K

    Final Undergraduate Semester Guidance

    I agree micromass, I never chose mediocre classes before for a GPA boost and I have never dropped a class. But, I thought that since the end of the undergraduate program is near and there are requirements for graduate school, I should make an exception. Austrian, the classes are Theory of...
  14. K

    Final Undergraduate Semester Guidance

    Hello all, I have a bit of a dilemma. I have two free electives to take and I am considering taking two "advanced" math classes and get a math minor or two semi-good classes from whatever. If I take two math classes and I get A's, it would be lovely. But, If I get low grades, my GPA will...
  15. K

    Prove Divisibility

    I like LaTEX. Why do you hate it?
  16. K

    Epsilon- Delta Proof

    Homework Statement Prove that ## lim_{x\implies 1} \frac{2}{x-3} = -1 ## Use delta-epsilon. The Attempt at a Solution Proof strategy: ## | { \frac{ 2}{x-3} +1 } | < \epsilon ## ## \frac{x-1}{x-3} < \epsilon ## , since delta have to be a function of epsilon alone and not include x. I...
  17. K

    Reflexivity Implies Symmetry?

    Wait, so my R is an equivalence relation then? Supposedly, it partitions the set into disjoint classes. I guess that my classes would be [1], [2], [3]? HallsofIvy, thank you for the clarification. I should have stated that in this case, it means the same.
  18. K

    Reflexivity Implies Symmetry?

    Nevermind. I just read somewhere that reflexive statements don't count towards symmetry. Apparently, it involves something like a diagonal class; I guess they pair this combinations in a matrix like form. Anyway. Thanks.
  19. K

    Reflexivity Implies Symmetry?

    Homework Statement Is this relation, R, on ## S= \{ 1, 2, 3 \} \\ R = \{ (1,1), (2,2) , (3,3) \}## Symmetric? It is obvious that it is reflexive.
  20. K

    Show F is Injective & Cardinality of Domain

    Now, I am wondering... do they have to be equal? a =2 and b =3. If the only restriction is that a,b ## \in \mathbb{N}## What would be an argument against what I just wrote?
  21. K

    Prove Divisibility

    Sorry, I got confused. Let's see: ## a\not | c \wedge a\not | b \implies a \not |bc ## ## pr \not = pqx \wedge qr \not = pqy \implies pq(r^2) \not = pqz## ## T \wedge T \implies F \equiv F## So, the statement is false.
  22. K

    Show F is Injective & Cardinality of Domain

    To show that ## g## is injective: ## g(a) = g(b ) \\ (a,1 ) = (b ,1 )## Then, ##a## must be equal to ## b## and ## g ## is injective. Thank you for the unique factorization explanation.
  23. K

    Prove Divisibility

    You are right, it is sufficient. Given your conditions, the converse technically would be true, since ##(F \wedge F \implies F) \equiv T## Am I right?
  24. K

    Co-Primes Proof

    Thank you very much, Curious. BTW, that cat in your pic looks happy :>
  25. K

    Prove Divisibility

    Homework Statement a.) Prove: If an integer ##a## does not divide ##bc##, then ##a## does not divide ##b## and ##a## does not divide ##c##. b.) State and either prove or disprove the converse of the above statement. The Attempt at a Solution a.) Proof by contrapositive ## a|c \vee a|b...
  26. K

    Co-Primes Proof

    So, d | n d =3 does 3 |n ? Well, the stipulations say that ##n## is not divisible by 3. ## n\not | 3 ## Sorry, but again I am lost. ## (n = 3k )\not = (3 \not = np), k,p \in \mathbb{Z} ##
  27. K

    Can I use induction?

    I see what you are doing. About what I wrote prior to this... I was talking about this supposedly property of absolute value ## |a-b| < c ##, then ## -c< a-b <c ##
  28. K

    Can I use induction?

    Wouldn't I need this first: ## -\sqrt{ a^2 + b^2} < (a-b) < \sqrt{ a^2 +b^2 }\\ ## Then, ## a^2 +b^2 < ( a-b )^2 = (a^2 - 2ab + b^2 ) < (\sqrt{a^2 +b^2})^2 = a^2 +b^2## Now, I don't understand
  29. K

    Can I use induction?

    uh, are you serious? ## (|a-b|)^2 = (a^2 - 2ab + b^2 ) \leq (\sqrt{a^2 +b^2})^2 = a^2 +b^2## Then the LHS will always be lesser for any ## \mathbb{R^+}##
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