Even if the argument doesn’t persuade them at the time it still makes sense to point it out to them so that they are (hopefully) aware of it later.

Vigier is pretty famous for making fretless guitars but they are also pretty pricey afaik. It’s not particularly hard to convert an existing guitar if you have any glass workers in your area willing to cut a mirror board.

I did roughly this way back in 2009 on a cheapo strat clone with a bolt-on neck:

1. Have a piece of mirror cut in the shape of the fretboard on the current neck.

2. Remove the frets from your old fretboard with pliers.

3. Fill the fret slots with wood filler.

4. Sand the whole thing down flat.

You can remove the fretboard entirely to swap it with the mirror board if you like, but sanding the whole thing down to the desired height seemed simpler to me at the time. You also retain vaguely useful “guide” marks from where the fret slots used to be with this approach.

Note that the height/width of your new board needs to play well with your nut/bridge height and whether or not you removed the old board. You also want a piece of mirror thick enough not to crack.

5. Epoxy the mirror board to the neck.

6. Sand off any excess epoxy and buff the sides smooth.

This approach worked okay for me at the time. I don’t recall any exact materials or measurements I used since I did this over a decade ago. I mostly just winged it and tried to use common sense.

I will say the whole process is pretty finicky. A lot of small things contribute to playability in general. Choice of strings (roundwound, flatwound, different gauges), nut/bridge height, truss rod adjustments, neck shims etc. There’s also the worry of cracking the glass from an overzealous truss rod adjustment and effectively breaking the whole neck (though this never actually happened to me).

The main issue I noticed playing fretless electric is that sustain is reduced. On a typical electric guitar the string vibrates between the metal fret and bridge materials (ignoring the nut). These materials are fairly hard, but on a fretless instrument the string vibrates between your much softer finger tips and the bridge. Perhaps a compressor pedal or some type of sustainer system would help?

If you pay attention to vigier recordings they tend to do really well with sustain. So their typical setup might be worth researching and trying to mimic.

For a toy DIY project to experiment with it’s fairly fun, but I wouldn’t expect anything game changing. Getting a nice sounding + nice to play set-up is challenging and involves a lot of nitty-gritty details.

As a side note, you could technically stop at step 4, though you’d probably want to sand things to a particular radius rather than flat. This is a common approach bass players take to convert fretted basses to fretless basses. There are many guides on how to do this online.

Disclaimers: This was something I did nearly 15 years ago as a teenager after reading quite a lot of random internet posts on it. Don’t use my rambling as a source if you decide to try this. Use a real guide (there are many for fretted to fretless bass conversion guides that would apply for the first 4-ish steps for example). I am not responsible for gear you break or money you waste.

You could also just buy a slide for cheap if you’re into that.

Hah no worries. Thanks for being so reasonable yourself lmao.

Fair points. The latter case is basically where my concern is.

I don’t have a don’t in this don’t.

I think you are assuming a level of competence from people that I don’t have faith people actually have. People absolutely can and do take “you cannot prove a negative” as a real logical rule in the literal negation sense. This isn’t colloquialism. This is people misunderstanding what the phrase means.

I have definitely had conversations with idiots that have taken this phrase to mean that you just literally cannot logically prove negated statements. Whether folks like you get that that is not what the phrase refers to is irrelevant to why I’m pointing out the distinction.

If you subscribe to classical logic (i.e., propositonal or first order logic) this is not true. Proof by contradiction is one of the more common classical logic inference rules that lets you prove negated statements and more specifically can be used to prove nonexistence statements in the first order case. People go so far as to call the proof by contradiction rule “not-introduction” because it allows you to prove negated things.

Here’s a wiki page that also disagrees and talks more specifically about this “principle”: source (note the seven separate sources on various logicians/philosophers rejecting this “principle” as well).

If you’re talking about some other system of logic or some particular existential claim (e.g. existence of god or something else), then I’ve got not clue. But this is definitely not a rule of classical logic.

Deconstructed calzone. Very rare and exotic.

The humble knifoon remains forgotten :(

The punchline here is a little compact. I don’t feel like it really gives the closure I need. Maybe if the basis for the joke had more continuity the humor would be less discrete.

Operating System Concepts by Silberschatz, Galvin and Gagne is a classic OS textbook. Andrew Tanenbaum has some OS books too. I really liked his OS Design and Implementation book but I’m pretty sure that one is super outdated by now. I have not read his newer one but it is called Modern Operating Systens iirc.

They don’t eventually become 1. Their limit is 1 but none of the terms themselves are 1.

A sequence, its terms and its limit (if it has one) are all different things. The notation 0.999… represents a limit of a particular sequence, not the sequence itself nor the individual terms of the sequence.

For example the sequence 1, 1/2, 1/3, 1/4, … has terms that get closer and closer to 0, but no term of this sequence is 0 itself.

Look at this graph. If you graph the sequence I just mentioned above and connect each dot you will get the graph shown in this picture (ignoring the portion to the left of x=1).

As you go further and further out along this graph in the positive x direction, the curve that is shown gets closer and closer to the x-axis (where y=0). In a sense the curve is approaching the value y=0. For this curve we could certainly use wordings like “the value the curve approaches” and it would be pretty clear to me and you that we don’t mean the values of the curve itself. This is the kind of intuition that we are trying to formalize when we talk about limits (though this example is with a curve rather than a sequence).

Our sequence 0.9, 0.99, 0.999, … is increasing towards 1 in a similar manner. The notation 0.999… represents the (limit) value this sequence is increasing towards rather than the individual terms of the sequence essentially.

I have been trying to dodge the actual formal definition of the limit of a sequence this whole time since it’s sort of technical. If you want you can check it out here though (note that implicitly in this link the sequence terms and limit values should all be real numbers).

I will fucking piledrive you if you mention AI again.

My degree is in mathematics. This is not how these notations are usually defined rigorously.

The most common way to do it starts from sequences of real numbers, then limits of sequences, then sequences of partial sums, then finally these notations turn out to just represent a special kind of limit of a sequence of partial sums.

If you want a bunch of details on this read further:

A sequence of real numbers can be thought of as an ordered nonterminating list of real numbers. For example: 1, 2, 3, … or 1/2, 1/3, 1/4, … or pi, 2, sqrt(2), 1000, 543212345, … or -1, 1, -1, 1, … Formally a sequence of real numbers is a function from the natural numbers to the real numbers.

A sequence of partial sums is just a sequence whose terms are defined via finite sums. For example: 1, 1+2, 1+2+3, … or 1/2, 1/2 + 1/4, 1/2 + 1/4 + 1/8, … or 1, 1 + 1/2, 1 + 1/2 + 1/3, … (do you see the pattern for each of these?)

The notion of a limit is sort of technical and can be found rigorously in any calculus book (such as Stewart’s Calculus) or any real analysis book (such as Rudin’s Principles of Mathematical Analysis) or many places online (such as Paul’s Online Math Notes). The main idea though is that sometimes sequences approximate certain values arbitrarily well. For example the sequence 1, 1/2, 1/3, 1/4, … gets as close to 0 as you like. Notice that no term of this sequence is actually 0. As another example notice the terms of the sequence 9/10, 9/10 + 9/100, 9/10 + 9/100 + 9/1000, … approximate the value 1 (try it on a calculator).

I want to stop here to make an important distinction. None of the above sequences are real numbers themselves because lists of numbers (or more formally functions from N to R) are not the same thing as individual real numbers.

Continuing with the discussion of sequences approximating numbers, when a sequence, call it A, approximates some number L, we say “A converges”. If we want to also specify the particular number that A converges to we say “A converges to L”. We give the number L a special name called “the limit of the sequence A”.

Notice in particular L is just some special real number. L may or may not be a term of A. We have several examples of sequences above with limits that are not themselves terms of the sequence. The sequence 0, 0, 0, … has as its limit the number 0 and every term of this sequence is also 0. The sequence 0, 1, 0, 0, … where only the second term is 1, has limit 0 and some but not all of its terms are 0.

Suppose we define a sequence a1, a2, a3, … where each of the an numbers is one of the numbers from 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9. It can be shown that any sequence of the form a1/10, a1/10 + a2/100, a1/10 + a2/100 + a3/1000, … converges (it is too technical for me to show this here but this is explained briefly in Rudin ch 1 or Hrbacek/Jech’s Introduction To Set Theory).

As an example if each of the an values is 1 our sequence of partial sums above simplifies to 0.1,0.11,0.111,… if the an sequence is 0, 2, 0, 2, … our sequence of partial sums is 0.0, 0.02, 0.020, 0.0202, …

We define the notation 0 . a1 a2 a3 … to be the limit of the sequence of partial sums a1/10, a1/10 + a2/100, a1/10 + a2/100 + a3/1000, … where the an values are all chosen as mentioned above. This limit always exists as specified above also.

In particular 0 . a1 a2 a3 … is just some number and it may or may not be distinct from any term in the sequence of sums we used to define it.

When each of the an values is the same number it is possible to compute this sum explicitly. See here (where a=an, r=1/10 and subtract 1 if necessary to account for the given series having 1 as its first term).

So by definition the particular case where each an is 9 gives us our definition for 0.999…

To recap: the value of 0.999… is essentially just whatever value the (simplified) sequence of partial sums 0.9, 0.99, 0.999, … converges to. This is not necessarily the value of any one particular term of the sequence. It is the value (informally) that the sequence is approximating. The value that the sequence 0.9, 0.99, 0.999, … is approximating can be proved to be 1. So 0.999… = 1, essentially by definition.

Some software can be pretty resilient. I ended up watching this video here recently about running doom using different values for the constant pi that was pretty nifty.

What exactly do you think notations like 0.999… and 0.333… mean?

Yes, informally in the sense that the error between the two numbers is “arbitrarily small”. Sometimes in introductory real analysis courses you see an exercise like: “prove if x, y are real numbers such that x=y, then for any real epsilon > 0 we have |x - y| < epsilon.” Which is a more rigorous way to say roughly the same thing. Going back to informality, if you give any required degree of accuracy (epsilon), then the error between x and y (which are the same number), is less than your required degree of accuracy

You are just wrong.

The rigorous explanation for why 0.999…=1 is that 0.999… represents a geometric series of the form 9/10+9/10^2+… by definition, i.e. this is what that notation literally means. The sum of this series follows by taking the limit of the corresponding partial sums of this series (see here) which happens to evaluate to 1 in the particular case of 0.999… this step is by definition of a convergent infinite series.

He is right. 1 approximates 1 to any accuracy you like.

Given that music boxes are very very old it is plausible that beethoven could have made a remark sharing his opinion on this exact issue. I don’t mean to agree/disagree with your point, I just find that kind of interesting.