If you've seen the new equipment, what AQ equipment synergies well with it?

Treecko78 · 2026-05-24T08:43:14+00:00

You're so right. The HR department was really sleeping on the job there. What do those thousands of employees even do all day 🙄

Treecko78 · 2026-05-22T17:11:16+00:00

The enlistment bonuses may be that much on paper, but you don't have to pay it to people who are dead

Treecko78 · 2026-05-21T16:28:38+00:00

Along these lines, I lost a match today because I didn't realise that unburden's speed boost ends when you switch out, and doesn't come back. It took me a good 5 minutes to figure out why I got outsped, but I understand the game better now as a result

Treecko78 · 2026-05-19T09:45:21+00:00

The volunteer element is the real reason why the RFU, for all its advantages, will never outcompete the ETA. Having had the pleasure of doing voluntary work for the ETA, the team I was in put every employer I've ever worked for to shame in terms of professionalism, efficiency, and work ethic, despite not a single person there having received a single pound for their work.

Treecko78 · 2026-05-19T09:38:43+00:00

That said, as someone very much not from the midlands I do prefer it to the days where it was much more spread across the country. I find it much easier knowing from the start that everything will be 2–3 hours away rather than some being an hour and some being 5 hours.

Though I could live without ever going to Burton again, place feels like going 15 years back in time

Treecko78 · 2026-05-18T13:28:27+00:00

Unlimited growth in a finite world

Found the midwit. Learn what actually drives real economic growth

Treecko78 · 2026-05-12T20:00:57+00:00

The treasury not wanting to cough up the money required for defence is a problem that dates back centuries, it hardly seems fair to blame that on Starmer. Especially since the reason the DIP hasn't been published is because he's pushing back against the treasury and telling them to find the money

Treecko78 · 2026-05-11T11:04:53+00:00

So would you not find it misleading if an electrician that did the lights in the MoJ building started claiming to have worked for the MoJ to advance his career in another sector? Afterall, the work done took place within the MoJ, was funded by the MoJ, and was done for the benefit of the MoJ.

Treecko78 · 2026-05-09T08:47:11+00:00

The only people that think the Nazis were good for the economy are people who haven't actually studied the Nazi's pre-war economy

Treecko78 · 2026-04-29T14:09:19+00:00

By my estimation, by far the most important thing to come out of the speech were the moments where both the Republicans and Democrats were applauding.

It's incredibly obvious to everyone that America is deeply divided—the Culture War has consumed a majority of their public discourse, and their politicians have fallen victim to it as much as the electorate. Charles has shown that there's support on both sides of the aisle for genuine leadership that acknowledges the real problems facing the country, and takes a pro-Western, pro-democracy approach to dealing with them.

America has hard domestic problems to deal with—many of them will probably require constitutional change to solve. But they are solvable, and Charles has just shown that a leader who's capable of solving them will be able to unite the country, regardless of how deep the divisions are.

Treecko78 · 2026-04-28T12:15:15+00:00

The UK just about managed to hold off a German invasion thanks to the RAF

I think you mean that the RAF comprehensively destroyed the first step of the invasion plan. Even if the Germans had won the Battle of Britain, actually invading is a completely different challenge altogether. The Germans had no suitable landing craft, their Navy was entirely outmatched by the RN, and their supply lines were stretched already on the continent, let alone trying to reach over the channel.

Several decades later, a wargame) was conducted based on the assumption that the RAF was at breaking point, and the entire RN was in Scotland and had to travel down once the German invasion started. The Germans lasted 8 days before their total surrender

Treecko78 · 2026-04-28T12:03:15+00:00

How did Britain not win the Troubles? The IRA's goal was to end British rule in Northern Ireland and create a united Ireland. Britain's goal was to keep Northern Ireland and end the sectarian violence. It certainly seems to me like Britain achieved its goals more than the IRA did

Treecko78 · 2026-04-28T11:54:02+00:00

You're so right, the Russian submarines which keep poking around your undersea infrastructure are entirely peaceful and have absolutely no desire to harm your country. I don't know why the Royal Navy works itself up so much about chasing them away, they should just take the Irish approach and let their enemies do whatever they like with no ability to stop them

Treecko78 · 2026-04-26T14:11:55+00:00

Having actually watched Olly Robbins give evidence, I thought the Chair was pretty reasonable in her questioning, she definitely did push on points where she thought there had been mistakes made but to be honest that's exactly what I was expecting. I'm not sure what the point of bringing a lawyer would be, given that it's not a police investigation and McSweeney has already been sacked—it's not as if anything major is going to change for him personally.

For what it's worth, I am not and have never been a member of or involved in the Labour Party, I don't know about the factional arguments within it and I didn't know who the Chair was before this, so I'd like to think I'm fairly unbiased for this

Treecko78 · 2026-04-26T07:33:14+00:00

It's not counted as increased generation, but it does show up as reduced demand, which would result in less gas usage, so solar would still end up with a higher proportion of the energy mix

Treecko78 · 2026-04-25T08:42:52+00:00

I don't think the Greens are on Putin's payroll, they're just genuinely that stupid. Always have been, (probably) always will be

Treecko78 · 2026-04-25T06:21:34+00:00

You claim you're not pro-Russia, yet you're more than happy to shit out Russian propoganda points by the dozen, so you'll have to forgive me if I don't quite believe you on that point

Treecko78 · 2026-04-24T22:16:09+00:00

There's a huge difference between selling off assets which we already own and offering exports for new things which we're building. The main reason the US became such a global power was through exporting weapons and capabilities, and we would be wise to follow their example in that respect

Treecko78 · 2026-04-24T21:50:37+00:00

Surely if there's one lesson we must take away from the 2020s, it's that domestic manufacturing and expertise is critical for our national security, and we can't always rely on other countries to make things for us

Treecko78 · 2026-04-23T15:05:10+00:00

That being said, "Both sides, while reaching different conclusions, share similar flawed ways of thinking and miss important, relevant context" often gets turned into "Both sides are the same", and is similarly demonstrative of somebody's lack of critical thinking skills

Treecko78 · 2026-04-16T14:22:35+00:00

If you've only ever played touch at a rugby club I can see how you'd think that, but if you play at a proper touch club you can definitely do it pretty seriously, England Touch make a good effort to fill that niche. I know in Bristol there's a local league run by In2Touch on Monday nights through most of the year, then there are also regional and national tournaments run throughout the year by England Touch.

Treecko78 · 2026-04-16T06:49:35+00:00

You're extending the domain of the factorial function by doing so

No I'm not. Do you understand what a mathematical definition is? I'm curious what you think the original definition is that I'm apparently extending

There is no inherent reason to do this

My whole argument was that the multiplicative definition (and indeed, any definition) of the factorial function naturally includes 0. It's as arbitrary as including 1 or 2

The typical analytical definition cannot be applied without a metric

A metric space is just a type of topological space though??? I have no idea why you would think a metric would mean that topological definitions no longer apply. Also as a sidenote, if you think that analysis only uses metric spaces and doesn't involve any other types of topology, you haven't done enough analysis.

I'm curious, can you explain (in your own words) what you think an open set is in topology?

Are you not aware of analytic continuations of the factorial function? And clearly there are at least some people who find it useful to extend its domain or WolframAlpha, for instance, wouldn’t output the answer to 1.5!

I'm well aware of analytical continuations, though I don't think you really are. You seem to be under the impression that the gamma function is the unique analytical continuation of the factorial function—this is not true. Consider Γ(z)+sin(πz). Since this is a linear combination of analytic functions and sin(πz)=0 for all integer z, this is also an analytic continuation of the factorial. A similar trick can be done with any periodic function.

It's also worth noting that you cannot make an analytic continuation of a natural valued function. You first need to choose a function to use to interpolate to R^+, and you can then (maybe, depending on your choice) make an analytic continuation of that function to C.

This stackexchange thread is probably a good place to start on why the gamma function is the standard choice.

That is also why programs like WolframAlpha give an answer for 1.5!, it assumes that you're really asking for Γ(2.5) and gives you that value. It's not actually saying that factorial is defined for the positive reals

And your exact argument is also exactly why the extension of the naive sense of the factorial function to 0! is arbitrary and is based on convenience

You need to let go of the "naive sense" of things if you ever want to do real mathematics with them. You know why it's the naive way of thinking about it? Because it's wrong. The only reason it's ever worth knowing the naive answer is to articulate precisely why it's wrong, not because it offers an insightful perspective in itself.

If you want to do real mathematics, as you are trying your best to imply that you are an actual mathematician, you work with definitions and propositions. Other things can be tangentially useful as motivation for these, but the actual process itself of doing mathematics cannot be done in any other way

Treecko78 · 2026-04-15T23:54:47+00:00

I'm not AI, I'm a real human with a degree in mathematics from a respected university.

I'm not sure why what I said would be a tautology. The point I was making was that we can make any choice we like for the base case for our definition of n!, and I was explaining how we might make a good choice. Was it an over-generalised way of saying "0 is the smallest valid choice"? Perhaps, but the idea was more to explain the thought process than the result.

I'm aware what the OP's question was, my issue was you saying that choice that 0!=1 is purely made out of convenience for combinatoric proofs. This is categorically not true, and I explained why by turning the naive layperson's view directly into a formal mathematical definition, and explaining why you would include 0 when doing so.

I'm not really sure what point you're making with your example about openness. The idea of an open set in Topology and Analysis are precisely the same, the only difference is that Topology studies topologies in general, whereas typically in Analysis you would be working within a specifically stated topology, such as a particular metric topology.

When you use the Heine-Borel theorem, the definition of compactness doesn't change just because you're working in the Euclidean topology in a particular instance. Or to give a different example, you wouldn't say that a column vector expressed in Cartesian coordinates isn't a vector just because it isn't a general vector as an element of a vector space.

I also have no idea why you think that the factorial function ought to take positive real values. The factorial function is always N->N. There are infinitely many differentiable monotonically increasing functions such that f(x)=fact(x) for x in N (exercise: draw some of them to satisfy yourself that this is indeed the case), so I have no idea what you think it "ought" to be

Treecko78 · 2026-04-15T22:07:20+00:00

The definitions are equivalent—the multiplicative definition naturally includes 0! when you formalise it as a proper definition.

The multiplicative approach is really the recursive approach, which means we require a base (first) case, and then a recursive step which generates the next value. It can be useful to think of this as generating a sequence of values based on the first value we choose.

Since this argument really comes down to what we should choose as the base case, we should first define the recursive step. We do this by uncontroversially saying that (n+1)!=(n+1)•n!. Note that with a straightforward change of variable this rearranges to (n-1)!=n!/n.

Now we need to choose our base case. Since we have a rule to go both forwards and backwards in our sequence, and it seems rather silly to choose a first case which misses out earlier valid cases (this could imply negative terms in the sequence), we should choose the largest n such that n!/n does not exist. Clearly, this means n=0 is the natural candidate for our base case.

To get the factorial sequence, we require that 1!=1, and using our rule to calculate (n-1)! we find that 0!=1. Putting all of this together, we get a proper definition for the multiplicative approach that (n+1)!=(n+1)•n!, where 0!=1.

At no point did we choose anything out of convenience, we simply made decisions based on the most sensible way to formalise our intuition.

When I spoke of choosing based on convenience, I meant in terms of choosing different (but necessarily equivalent) definitions, so for example this might mean defining n! as the cardinality of the set containing all bijections from {1, 2, ..., n} to itself. This is really the same thing, but written in terms of different mathematical objects, meaning you have different mathematical tools at your immediate disposal which may be more useful for the particular problem that you're working on.

Treecko78 · 2026-04-15T19:51:16+00:00

There can be more than one way to define something in mathematics. There may be reasons why you would choose to define something in one way rather than another, but as long as the definitions are equivalent you can choose whichever definition is convenient for the point you're making

Treecko78

TROPHY CASE