Recent content by Ciaran

Hello, I wonder if anyone could settle a disagreement I'm having with one of my peers. The question is 'How many surjective functions are there from a set of size n+3 to a set of size n?'. Now, I've already proven that there are (n+1 choose 2)n! surjective functions from a set of size n+1 to a...

Really? That seems quite messy and bitty! What did you get as your answer? I started off with mgsinθ +mRω^2 cosθ = μmg cosθsinθ and simplified for omega from there

Is it just a_ perp= (N/m)- gcosθ and a_ parallel= gsinθ- (F_f/m) ? And for c), I get ω= sqrt( (g/R)(μsinθ- tanθ))

Ahh I see, I can see how it could lead to confusion! But then how am I meant to derive 2 expressions for acceleration if I have unknown forces? I don't know how to express the friction or the normal force

So, vertically, the component of centripetal force is the normal force minus mgcosθ. And, parallel to the slope, the component of centripetal force is mgsinθ minus the unknown frictional force?

So for parallel to the slope, I have a= g sinθ (1-µ) as force up slope= force down slope as it isn't moving. For vertically, I feel like I'm missing something because isn't it just zero?

Hello! I do indeed get the expression needed ! So for b), do I need to use the two components of the acceleration from part a)? And for c), do I simply need to consider the component of weight down the slope, the centripetal force and the force of friction?

Hi there, I've come across the following question and drawn a free body diagram: A wedge with face inclined at an angle θ to the horizontal is fixed to a rotating turntable. A block of mass m rests on the inclined plane and the coefficient of static friction between the block and the wedge is...

My apologies, I have only now just noticed you replied! f(x) was meant to be surjective from N to Z and g(x) was meant to be injective from Z to N

Homework Statement A wedge with face inclined at an angle theta to the horizontal is fixed on a rotating turntable. A block of mass m rests on the inclined plane and the coefficient of static friction between the block and the wedge is μ. The block is to remain at position R from the centre of...

Ahhh, what about f(x) = x/2 if x is even, (1-x)/2 if x is odd. And g(x)=2x+1 for positive x, -2x for negative x?

I'm pretty sure g(x)= x! and f(x)=x^2 are injective and surjective, respectively

It's the conditions that are proving to be tricky to me- for the surjective function, does it mean my function can only generate integer values ?

Oh I see, I was asking for 2 separate functions- I was asked by my instructor to find a solely injective function from Z to N and a solely surjective function from N to Z. I was struggling so wondered if there was some way of generating one such that I didn't just have to think of a function...

Hello! Thanks for the reply- the function is injective but not surjective. What about surjective from N to Z and is there some algorithm for generating a function satisfying such conditions?