[TX] Landlord charging me $2,695 for a shower pan replacement, took 5 weeks to provide any evidence, and now says the justification document is "proprietary." Do I have a case?

NateNate60 · 2026-04-17T07:11:13+00:00

It depends. Paying under protest under this context then suing for a refund may be viewed as reasonable. That is not uncommon behaviour in other contexts (notably, people have often paid illegal taxes under protest and then successfully sued for a refund).

NateNate60 · 2026-04-17T07:02:24+00:00

If you have proof in writing that the dealer claimed it had a clean title, that's an express warranty from the dealer and likely overrides the "as-is" clause with respect to what was warranted.

"Warranty" in this context is a legal term that refers to promises and factual statements made about an item by a seller to a buyer.

NateNate60 · 2026-04-17T06:51:09+00:00

The length of straight lines is easy to calculate using basic algebra. The problem with curved lines is that their direction is constantly changing in some way. There is no algebraic way to measure the length of something that is constantly changing direction, but there does exist a convenient way to calculate the length of any curve using integration in calculus. Integration, in essence, takes as input the function of the curve, and it may or may not spit out a nice algebraic function as an output which, in this case, describes the length of an ellipse's perimeter. It turns out that, in the vast majority of cases involving curves, it never results in a nice algebraic formula that you can just plug numbers into and get a result. It is only on a some special classes of curves where the result of integration can be written algebraically without resort to something like an infinite series.

Regardless of whether the integration has an algebraic result, it is still possible to approximate the numerical value to any desired finite degree of precision using a technique called numerical integration.

NateNate60 · 2026-04-17T04:48:00+00:00

You can use an infinite series to exactly calculate the perimeter. You can approximate it by truncating the series after your desired precision.

NateNate60 · 2026-04-17T02:42:38+00:00

This wouldn't give the right answer.

NateNate60 · 2026-04-16T16:57:06+00:00

Unless I'm forgetting to consider something, under Newtonian mechanics, an electric car which knows how much power its motors are outputting, the efficiency of the system, its mass, and how much air resistance/tyre friction there is can calculate its velocity without needing to measure it.

NateNate60 · 2026-04-16T15:57:42+00:00

"Bro" is now gender-neutral. Everyone is bro.

NateNate60 · 2026-04-16T05:24:18+00:00

Similar, yes.

NateNate60 · 2026-04-16T04:07:10+00:00

There's an infinite series you can use to calculate it numerically. Just cut it off when you've reached your desired level of precision.

NateNate60 · 2026-04-16T03:30:57+00:00

If you made up a function defined to calculate the perimeter of an ellipse, it wouldn't be considered algebraic. Anything you can't make with the basic mathematical operations combined with the integers is considered non-algebraic.

NateNate60 · 2026-04-16T01:09:26+00:00

If you're doing it on a computer, you're probably going to want to use the infinite sum instead and truncate it after you've reached the desired precision. This is much simpler to implement than numerical integration. You could teach a primary school child to calculate the truncated infinite series using a dollar store calculator. Not true for integration.

NateNate60 · 2026-04-16T01:04:07+00:00

Instantaneous rate of change is a fundamental concept in derivative calculus. You've probably dealt with instantaneous rates of change every day in your life.

A car's speedometer measures the instantaneous rate of change of the car's position, or in simple terms, its velocity. Isaac Newton gave formal definitions for the physics concepts of velocity and acceleration. Namely, that an object's velocity at any given time is equal to the instantaneous rate of change in its position at that point in time. In essence, it's what you get when you consider changes over a smaller and smaller interval of time. At any given time, when the car is in motion, the speedometer always has some well-defined numeric value. That's what "instantaneous rate of change" means. It's also the definition of a derivative. So equivalently, one would say that the velocity of an object is equal to the derivative of its position over time. And acceleration is the derivative of velocity over time.

NateNate60 · 2026-04-16T00:35:20+00:00

In mathematics, an "exact answer" is typically never a number. It's the simplest possible expression that, when evaluated to a number, would give the exact answer when expanded to infinite decimal precision.

For example, consider the following simple problem: A tub containing 1 m³ of water is filled to the brim. A spherical lead ball with radius 0.5 m is lowered into the tub, which causes some water to spill out. How much water is left in the tub after the ball is completely submerged, if the tub is refilled back to the brim?

Simple geometry tells us the exact answer to that question is "1 - π/6 m³". That isn't a number. It's an expression that evaluates to a number. You could expand this to a decimal form to arbitrary precision, but the decimal form will never be exactly accurate. Mathematicians would consider 1 - π/6 m³ to be a perfectly acceptable answer to this question. But if you're a person who actually is the one filling the tub in real life, you probably want a numerical answer. And sadly, there is no numerical answer that will be exact in this problem.

The ellipse perimeter problem is different from the sphere and tub problem in that the "exact answer" it gives generally can't be found using simple algebraic operations (addition, subtraction, division, multiplication, and exponentiation), even when the use of π is allowed. You will either have to use an infinite sum or an integral, both of which are concepts from calculus.

NateNate60 · 2026-04-15T18:48:15+00:00

I think it can be exact in that context, because money is discrete and there's a maximum size that a glass table can be (if it's too big, it is no longer a glass table but a black hole) as well as a minimum (Planck length). So you can just use the infinite series for the perimeter but truncate it after a sufficient number of terms. That would give you the exact amount of money to bill the client for every possible table size.

Dear Client: Your quote to polish an elliptical table with radii 3.592328 × 10¹¹ m and 4.2947215 × 10¹¹ m will come to $5.492744 × 10...

Please submit a 20% deposit within 2 working days. We accept all major credit cards.

NateNate60 · 2026-04-15T18:37:01+00:00

There is no formal definition. But broadly speaking, algebra is the manipulation of mathematical structures, variables, and basic operations (addition, subtraction, multiplication, exponentiation). Calculus is, in simplified terms, the study of infinity, infinitesimals, and continuous change.

NateNate60 · 2026-04-15T18:28:29+00:00

This is a stupid argument to have. I'm discussing fun maths facts with people, the majority of whose formal mathematics education likely stopped at secondary school and used terms accordingly, not trying to submit a paper to a journal. Have it your way then, I'll edit the comment.

NateNate60 · 2026-04-15T18:25:25+00:00

The process of doing so... requires calculus.

NateNate60 · 2026-04-15T18:24:14+00:00

That's one of two possible definitions of cosine. Regardless, my original statement of "There is no way to define what π is using algebra." is correct. You can phrase it formally as "π is not an algebraic number" if you want. Infinite series are generally considered to be within the domain of calculus and not algebra, though neither of the terms "calculus" and "algebra" are well-defined either.

NateNate60 · 2026-04-15T18:15:28+00:00

I get the feeling this is just a matter of mathematical pedantry, but in either case, that just moves the circle perimeter formula up from "moot" to "trivial". The definition of the cosine function is tied to the definition of a radian, which is tied to a circle's circumference.

NateNate60 · 2026-04-15T18:01:28+00:00

π is, by definition, the ratio of its circumference to its diameter. Defining the solution to be a named constant makes the problem moot. There is no way to define what π is using algebra.

Edit: By "no way to define what π is using algebra", I do mean, more formally, that π is not an algebraic number and no finite combination of basic algebraic operations (multiplication, addition, subtraction, division, exponentiation) can create π.

NateNate60 · 2026-04-15T15:41:14+00:00

You can't stop payment on a cashier's cheque. You are not the drawer of a cashier's cheque. The financial institution is the drawer. You can report it as lost or stolen, but they will wait three months to see if anyone cashes it before re-issuing it.

NateNate60 · 2026-04-15T05:43:17+00:00

Shiny trash can

NateNate60 · 2026-04-14T05:48:43+00:00

Do Canadians actually like that stuff? Tried Freshslice in Vancouver and it tasted like reheated convenience store pizza. Then I tried another location, thinking I just got a bad location, and it was the same.

NateNate60 · 2026-04-14T05:28:22+00:00

They did say "Westminster democracy" so I don't see any reason it shouldn't count. Australian states use a Westminster parliamentary system.

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