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Is it normal to spend 40 minutes stuck on one proof problem

Forty minutes on a proof you have not seen the shape of before is completely ordinary and often on the fast side. Computation problems have a time you can estimate. Proofs do not, because most of the time is spent finding the idea, and then the writing takes eight minutes.

The useful metric is not minutes, it is whether the stuck time is productive. Circling the same dead end for 40 minutes is bad. Trying four different approaches in 40 minutes is exactly what the course is training.

264 · in/math-help ·

What does a full set of gear realistically cost in the UK if I want AA rated and not to boil in July

Supermarket special buys and end of season clearances are how I kitted out my partner for a little over 300 total. The trick is knowing your sizes from a shop first, then buying when the discount lands, because bike gear sizing is wild between brands. Two of the four items were fine, the gloves were terrible and got replaced within a year, which still left us ahead.

112 · in/motorcycle-gear ·

I cook dinner without a recipe but every cake I bake is dense, what is actually different?

The difference is feedback. Cooking is a loop: you taste, you adjust, you correct right up to the plate. Baking is a single irreversible reaction where you assemble a structure, put it in a box, and find out 40 minutes later, so all your skill at correcting has nowhere to act. Everything you described is a structure error rather than a flavour one. Microwaved butter is partly melted, which means it will not hold the air you are trying to beat into it, and mixing until smooth is mixing past the point where the gluten stops helping and starts making it tough. Butter at cool room temperature, beat until visibly paler, and stop the moment the flour disappears.

129 · in/cooking-technique ·

Setup is paid for, what does one hive actually cost me every year after that?

I keep a spreadsheet, so here is my recurring list by category rather than by price, since prices differ everywhere. Mite treatment twice a year, and I use two different chemistries to rotate. Sugar for autumn feeding, which for a single hive is a few large bags and is by far the cheapest way to keep a colony alive over winter. Foundation for maybe ten frames a year as I rotate out old dark comb on a rough four year cycle. Replacement gloves, because they get sticky and torn. A new smoker every few years.

Jars, lids and labels genuinely cost more than everything above combined for me, because a good harvest turns into a lot of glass. If you sell any of it, that flips the arithmetic entirely and the hive starts paying for itself.

128 · in/backyard-bees ·

First paying customer wants a feature only they would ever use

At three customers you do not have a roadmap, you have a hypothesis and a customer telling you it is wrong in one specific way. Build it, but build it as a negotiation rather than a favour.

What I would ask for in exchange:

  • an annual contract paid up front rather than monthly, which prices the three weeks properly
  • a written case study or a reference call once it works
  • the right to offer the integration to other customers

If they will not do any of the three, that tells you how much they actually want it. And genuinely ask them how they do it today, because sometimes the real request is smaller than the integration they asked for, a CSV export on a schedule instead of a live sync.

512 · in/startup-traction ·

How do I choose delta in an epsilon delta proof without just guessing

You find delta by working backwards, on scratch paper, and then you write the proof forwards. Those are two separate documents and your textbook only shows you the second one.

Scratch: start from what you want, |f(x) - L| < ε, and manipulate until you have |x - a| < something. For f(x) = 3x + 1 at a = 2, |3x + 1 - 7| = 3|x - 2|, and you want that under ε, so |x - 2| < ε/3. That is where delta came from.

Proof: let δ = ε/3, assume 0 < |x - 2| < δ, then |f(x) - 7| = 3|x - 2| < 3δ = ε. Done. Nothing mysterious, just the scratch work read right to left.

331 · in/math-help ·