Consider the function $\theta:\{0,1\}\times\mathbb{N}\rightarrow\mathbb{Z}$ defined as $\theta(a,b) = a-2ab+b$. Is this function bijective?

For injective, I tried doing the contrapositive by supposing $\theta(a,b)=\theta(c,d)$, then $a-2ab+b=c-2cd+d$, but I have no idea where to go from there. I tried solving for a and b separately and plugging it back in, but that just turned into a huge algebraic mess.

I haven't figured what I'm going to do for surjective yet.

I'm not very good at this subject, so sorry if this is a stupid question. Any hints are appreciated, thanks.


Question: Is a self cleaning lube enough for chain maintenance?
Answer: I've used white lightening and thought it was good. I never use oil based lubes now - they're just too messy and you end up paying double because you need to first buy the oil and then also buy expensive degreaser to wash them off again.

I do get through wax based lubes faster than oil - you have to reapply more often. Compared to the faff of oil based lubes though, it seems worth it.

You do have to still clean your chain and cogs off every so often. How often depends on the weather, distance and type of terrain you've been cycling through. But, it seems like far less mess and time is required than oil based lubes. To clean I soak the chain in a mix of hot water, washing up liquid and something like kitchen/hob surface cleaner.

I think my girlfriend appreciates it too as I make less of a mess when doing any bike maintenance.

I forgot how nasty oil based lubes can be until recently when I stopped on a trail to help a guy with a broken chain. His chain was gunked up nastily. The oily emulsion looked like it held particles of grit in it well, so I'm sure he was grinding through his chain and transmission with it. Also, I gave up trying to wash the stuff completely off my hands after I got home, and ended up with marks that lasted a few days until my body shed a layer of skin. I wouldn't have had that problem if he'd used a wax based lube.