Recent content by sophiecentaur

Good to get a tick / check. I only recently found that smiley. Have I been unobservant for years?

Shame but I'd guess that lava tubes would be very few and far between. Also, are we sure that they would form in the same way that they form under full gravity. Maybe volcanoes would be higher and that could make the flows very different and the lava could solidify quicker (or slower).

Yes. It's fine with me. I believe the the relationships between all the axioms in the Maths we use have been sorted out and are consistent. It always makes me uneasy when trying to think just how this relates to the real world, though. But that's all Philosophy and PF doesn't deal with it. It's...

I could go for that, except that wouldn't you have to test every function for continuity over all its range? for a function we know to be discontinuous at certain values - say tan(x), you can test near your π/2 point and the test would show up the discontinuity pretty quickly. You seem to be...

I think this is where our little 'skirmish' started. Can you not show that our function is continuous by finding the limit when x=0+∂x as ∂x →0. Why should the function be discontinuous only at (0,1) ? ps No wonder ; we were both looking at the same site and both saying that it makes perfect...

Would this link help? It leads into the 'my terminology' link above and introduces the concept of Lim (Limit). In your pure Maths course, you must have come across that idea. That idea of finding a final value as the limiting value as another variable approaches (say) zero. I really don;t see...

In which case you will understand how I'm using the concept of limits in this case. Afaik, my terminology is pretty well understood and accepted. Are you talking about something different?

The software programming is pretty well the easiest part of your project. Your main problem is what to contain the electronics in and how to secure it all. You will need a display and buttons unless you intend to use your phone to control it all. Your container and the wiring needs to ve VERY...

Pure or applied Maths course? The Pure Maths guys look after the souls of Scientists and engineers etc. who use Maths for their work. Your terminology is a bit approximate and it's not getting us anywhere. I'm afraid that, unless you are a 'good' pure mathematician, you need to trust their...

There's quite a high level of sophistication about rational indices. Also even for all arithmetic with rational numbers; we tell kids about 'sharing' and division but even that is a matter of going through the motions and believing you got a right answer. As a lifetime Engineer, I'm used to a...

If you want to have a valid opinion or objection to this stuff then you need to do what I did (or read and follow through a good book. If not then you have to accept some "authority". The concept of a limit is more than just your single example. Neither of us knows enough to do more than accept...

You want an arm waving reason? Maths isn't an arm waving topic. In the late 60s, I did a Maths Analysis course at Uni. There were ten (or maybe twenty) hourly lectures and it was scrupulous at every step, from what do we mean by Zero, One , forms of Infinity etc., to hard stuff where I fell...

Or, more accurately, The limiting value for y as x approaches zero is one.

Hardly an arbitrary choice; for the function to be continuous, the value at zero has to be 1.

You have to apply that logic to a well defined situation. It's true, only when the floor is horizontal and if the tv is not going round a curve or accelerating / braking. Also, of course, the weight inside must be distributed evenly - no heavy bits in there, like a large transformer, off centre...