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Toby Bartels @tobybartels.bsky.social · 17m

Sad that the Peace Prize is being given to such a piece of shit too. I mean, if it came down to her or Trump, then obviously Trump is the worse choice. But she's a traitor to her people for praising the American dictator who persecutes them, just because he pretends to oppose their own dictator.

María Corina Machado on X: "This recognition of the struggle of all Venezuelans is a boost to conclude our task: to conquer Freedom. We are on the threshold of victory and today, more than ever, we count on President Trump, the people of the United States, the peoples of Latin America, and the democratic" / X

This recognition of the struggle of all Venezuelans is a boost to conclude our task: to conquer Freedom. We are on the threshold of victory and today, more than ever, we count on President Trump, the people of the United States, the peoples of Latin America, and the democratic

x.com

Toby Bartels @tobybartels.bsky.social · 1h

MAGA religious freedom means the freedom to impose their religion on everyone else, not the freedom for anyone else to practise their religion.

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Toby Bartels @tobybartels.bsky.social · 1h

Hiding inside the building apparently: bsky.app/profile/long...

LongTime🤓FirstTime👨‍💻 @longtimehistory.bsky.social · 4h

Full statement issued by the Hoffman Estates Police Department. ⬇️

"All of this information can be found on our website at hoffmanestates.org."

Reposted by Toby Bartels

Alan Dettlaff @alandettlaff.com · 4h

Yesterday I was told that the class I’m scheduled to teach this month, Confronting Oppression & Injustice, is no longer part of our curriculum. This is a required class yet there was no discussion, no faculty vote, just an email saying the class no longer exists. This is what it’s like in Texas now.

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Toby Bartels @tobybartels.bsky.social · 5h

The article is in a libertarian magazine, so I guess the writer is principled. But the commenters underneath … whoo! Pretty typical for that comment section unfortunately.

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Toby Bartels @tobybartels.bsky.social · 1d

PS: I know this thread is almost five months old, but people have been reviving it at the top level, so I'm reviving it here.

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Toby Bartels @tobybartels.bsky.social · 1d

And people do prove it, but they pretend that they're proving something only about +: that it's well-defined. But really it's a theorem about + and = just like the first theorem is a theorem about + and <.

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Toby Bartels @tobybartels.bsky.social · 1d

With real numbers for example, nobody has any problem defining x<y and then proving neat theorems like x<y → x+z<y+z. But when you define x=y in a similar way, you can't then treat x=y → x+z=y+z as an axiom; it too needs to be proved as a theorem.

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Toby Bartels @tobybartels.bsky.social · 1d

The problem is simultaneously defining equality by an arbitrary equivalence relation *and* treating equality as a fundamental logical notion. These two kinds of equality are (to be meta for a bit) not the same.

(1/3)

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Toby Bartels @tobybartels.bsky.social · 1d

(This is because automorphisms preserve the integers and thus the rational numbers; and they preserve order because this is definable from the ring structure, since precisely the squares are positive.)

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Toby Bartels @tobybartels.bsky.social · 1d

I'm late to this discussion (because I'm looking at quote-skeets of Rochelle's ‘what are two things equal? never’), but …

You can just work with the ring structure; ℝ has no nontrivial ring automorphisms.

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Toby Bartels @tobybartels.bsky.social · 1d

Alternatively, throw in the complex-conjugate operation (or equivalently the real-part function). This preserves the nontrivial automorphism that deserves to be there (holding the plane upside down) but gets rid of all those BS automorphisms that you can only construct with the Axiom of Choice.

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Reposted by Toby Bartels

julia 🦄 @hypv.bsky.social · 1d

A lot of people think that the complex numbers are more nicely behaved than the real numbers. But in fact ℝ is better than ℂ, and model theory and Gottfried Wilhelm von Leibniz can help us to understand why. Part 1/2 #MathSky

$\title{Why $\mathbb R > \mathbb C$, and how model theory can help explain why} \author{Julia Redacted} \begin{document} \begin{frame} \titlepage \end{frame}$ $\begin{frame}{How do you tell when two things are different?} Mathematicians love to gloss over this, but it's \highlightv{really hard} to tell whether two things are equal. One object can be presented in different ways and it can be non-trivial to see they give the same thing. \bigskip \begin{itemize} \item If you were ever confused why $1 = 0.999\ldots$ you've experienced this. \end{itemize} \bigskip If you're interested in some mathematical structure \highlightb{$\Mcal$} consisting of objects, how do you tell them apart? \end{frame}$ $\begin{frame}{Leibniz's Identity of Indiscernibles} \begin{columns} \begin{column}{0.2\textwidth} \includegraphics[width=0.75in]{leibniz.jpg} \end{column} \begin{column}{0.8\textwidth} \highlightp{\textbf{\Large``}}Two objects are identical iff they have the same properties.\highlightp{\textbf{\Large''}} \vspace{.5in} \end{column} \end{columns} \begin{columns} \begin{column}{0.8\textwidth} \ Mathematically: $x$ and $y$ are objects in $\Mcal$. Then $x = y$ iff $\Mcal \models \phi(x) \iff \Mcal \models \phi(y)$ for every property $\phi$. \begin{itemize} \item $\Mcal \models \varphi(x)$ is model theorist speak for \highlightv{$x$ has property $\varphi$ in the structure $\Mcal$}. \item It's circular to have a property like ``identical to $x$''. We only mean properties you can express in the \highlightv{language} of the structure, e.g. the language of rings. \end{itemize} \end{column} \end{columns} \end{frame}$ $\begin{frame}{Telling numbers apart} \begin{itemize} \item You can distinguish $1$ from any other number, because $1$ is the only number which is a multiplicative identity. \item You can distinguish $\pi - e$ from $\pi/e$ because one is negative and the other is positive. \item You might think you can distinguish $i$ and $-i$ because only one is on the top half of the complex plane, but what if you are holding $\Cbb$ upside down? \end{itemize} \end{frame}$

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Reposted by Toby Bartels

Erik Loomis @erikloomis.bsky.social · 1d

This Day in Labor History: October 10, 1917. The red light district of New Orleans, known as Storyville, closed due to the efforts of reformers seeking to eliminate vice from the city. Let's talk about sex work and how banning red light districts just made workers unsafe!

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Toby Bartels @tobybartels.bsky.social · 1d

The thread isn't finished yet; it still could be!

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Toby Bartels @tobybartels.bsky.social · 1d

Cops shooting dogs is a national pastime here in the USA (dozens every day).

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Reposted by Toby Bartels

Thomas Zimmer @thomaszimmer.bsky.social · 2d

We need to talk about Russell Vought – But Properly

Why certain mainstream outlets insist on sanitizing Vought as a devout “small government” conservative – and what actually animates his war against pluralistic democracy.

Some thoughts from my new piece:

🧵

We need to talk about Russell Vought – But Properly

Why certain mainstream outlets insist on sanitizing Vought as a devout “small government” conservative – and what actually animates his war against pluralistic democracy

steady.page

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Toby Bartels @tobybartels.bsky.social · 2d

[*] The official pay date isn't until Wednesday, but direct deposit is usually available the previous Friday, so people relying on that will get hit first. Source: www.gsa.gov/buy-through-...

2025 payroll calendar

Get a printable version of the calendar, view the color-coded symbols for remarkable dates, or get a textual equivalent of remarkable dates.

www.gsa.gov

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Toby Bartels @tobybartels.bsky.social · 2d

They aren't supposed to be, but on the other hand, nobody's actually missed any pay yet. It's tomorrow[*] when the first shit hits the fan, and we'll see how agents react then.

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Reposted by Toby Bartels

America's Voice @americasvoice.bsky.social · 3d

"While new moms worry about formula for their infants and furloughed federal workers stress about next month’s rent or mortgage, the administration’s mass deportation obsession will continue uninterrupted," writes @tusk81.bsky.social

This says everything about this administration’s priorities.

ICE Rages On During Shutdown As Federal Workers Go Without Paychecks and American Kids Face Potential Hunger

Priorities.

americasvoicecnn.substack.com

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Toby Bartels @tobybartels.bsky.social · 2d

Me too, but public opinion is the aggregate of all of the ‘just some guy’s out there, so it matters.

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Toby Bartels @tobybartels.bsky.social · 2d

Not at all. Here's their board of directors. A bunch of CEOs and EVPs, not a single journalist. It's not clear from their bios whether any of these has *ever* been a journalist. www.newsmediaalliance.org/about-us/boa...

2024-2026 News/Media Alliance Board of Directors | News/Media Alliance

www.newsmediaalliance.org

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Toby Bartels @tobybartels.bsky.social · 2d

it's an organization of the *owners* of commercial news media, not the journalists or the readers. I'm sure they're only too happy with someone who defunds the nonprofit alternative.

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Toby Bartels @tobybartels.bsky.social · 2d

Yeah, there's probably an argument that this particular prisoner shouldn't have access to this particular app. But tons of ordinary prisoners would be (and in many cases are) devastated to lose access to their friends and family on Facebook.

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Reposted by Toby Bartels

Prem Thakker ツ @premthakker.bsky.social · 3d

My gosh. After the US bombed multiple boats in the middle of the ocean, murdering people on grounds that they were allegedly "carrying drugs," the US Attorney General says "Just like we did with cartels, we're going to take the same approach, President Trump, with Antifa."

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