YTG123 @ ytg @sopuli.xyz

I often use tone tags, so in their absence, try to interpret everything I s

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1 yr. ago

Using "Next"

So true! I can also confirm it happens cross-linguistically

Surely the US government won't like that if they're US citizens, right?

that can’t stop giving her money

well… I mean… you don't have to

For any a, b, c, if a = b and b = c, then a = c, right? The transitive property of equality.
For any a, b, x, if a = b, then x + a = x + b. The substitution property.
By combining both of these properties, for any a, b, x, y, if a = b and y = b + x, it follows that b + x = a + x and y = a + x.

In our example, a is x' (notice the ') and b is 0.999… (by definition). y is 10x' and x is 9. Let's fill in the values.

If x' = 0.9999… (true by definition) and 10x = 0.999… + 9 (true by algebraic manipulation), then 0.999… + 9 = x' + 9 and 10x' = x' + 9.

if you are rearranging algebra you have to do the exact same thing on both sides

If you actually change any of the sides. Since, after substitution, the numeric value doesn't change (literally the definition of equality), I don't have to do anything – as I'm not rearranging. I'm merely presenting the same value in an equivalent manner. By contrast, when multiplying both sides by 10, since multiplication by 10 changes the concrete numeric value, I have to do it on both sides to maintain the equality relation (ditto for subtracting x'). But substitution never changes a numeric value – only rearranges what we already know.

(Edit)

Take the following simple system of equations.

 latex

    
5y = 3
x + y = 6

  

How would you solve it? Here's how I would:

 latex

    
\begin{gather*} %% Ignore the LaTeX boilerplate, just so I could render it
\begin{cases}
y = \frac{3}{5} \\ % Isolate y by dividing both sides by 5
x = 6 - y % Subtract y from both sides
\end{cases} \\
x = 6 - \frac{3}{5} \\ % SUBSTITUTE 3/5 for y
x = 5.4 \\
(x, y) = (5.4, 0.6)
\end{gather*}

  

Here's how Microsoft Math Solver would do it.

The substitution property of equality is a part of its definition; you can substitute anywhere.

Similarly, 1/3 = 0.3333…
So 3 times 1/3 = 0.9999… but also 3/3 = 1

Another nice one:

Let x = 0.9999… (multiply both sides by 10)
10x = 9.99999… (substitute 0.9999… = x)
10x = 9 + x (subtract x from both sides)
9x = 9 (divide both sides by 9)
x = 1

Interesting that an Israeli newspaper provides a more balanced report than US outlets… how did that happen?

I’m pretty sure that would be ex uno, plura

They did cooperate with authorities, but they also took their time in disclosures to explain precisely what the user did wrong, and how you can avoid making the same mistakes. At the end of the day, Proton only has the information you provide them. And if you don't encrypt your stuff, it's not safe.

No option to disable… that I found, that is.

Mine provides a connection, but doesn’t expose ports on v6. So I can access v6 services but can’t self-host any.

School teachers. Not deliberately, but there is a shortage of them here.

supporting a terrorist organization

Also a serial traffic offender. Not really that important but quite ironic as he is responsible for the police.

What do you mean "fuck them", they don't exist any more...

Are there people on Lemmy defending the bombing of Palestinians because of various reasons?

Protests were calling for years for Netanyahu to go to The Hague. Is it happening?

There’s a known Plasma 6 bug causing some weirdness at the bottom of the screen, but I expect it will be fixed soon. In any case, switching between virtual desktops gets rid of it.

Does M3/M4 support AV1 encoding?

But you can never know if they pronounce them right :(

Then again, Tolkien does describe the pronunciations in enough detail in the Appendix to LOTR (I don't know if it's in every edition though).

You can use negative decibels, right? It's a logarithmic scale