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Daniel Marans on X: "New: In VA-10's Democratic primary, ..." / X Donation To Pro-Israel Group In Virginia House Race Shows Limits Of Campaign Finance Laws | HuffPost Latest News - "Democrat Eileen Filler-Corn gave the Democratic Majority for Israel PAC $110,000 a day after the group endorsed...

VA-10? Incumbent Jennifer Wexton has decided to quit because she has a disease much like Parkinson's disease: Progressive Supra-nuclear Palsy Wexton Shares Health Update and Announces Retirement Plans | U.S. House of Representatives Virginia's 10th Congressional District - Ballotpedia Virginia...

Who could replace Joe Biden? Here are six possibilities | Joe Biden | The Guardian Kamala Harris, Gavin Newsom, J B Pritzker, Gretchen Whitmer, Sherrod Brown, Dean Phillips Biden meets with his family amid pressures to step down after debate | Joe Biden | The Guardian - "Officials dismiss...

...It uses Euler's totient function - for positive integer n, phi(n) is the number of positive integers coprime or relatively prime to n. phi(n) = n * product of (1 - 1/p) over p: all the distinct prime factors of n The theorem itself: for a and n coprime, a^(phi(n)) = 1 mod n That means...

Rational numbers have the property that their decimal or other place-system representations have infinitely-repeating sequences of digits that trail the first digits. I'll show three repeats of each repeated sequence. Decimal: 1 - 1.000... 2 - 0.5000... 3 - 0.333... 4 - 0.25000... 5 -...

real analysis - Do the Liouville Numbers form a field? - Mathematics Stack Exchange Absolutely not, because an algebraic field needs an additive identity and a multiplicative one: 0 and 1 for the rational numbers and their supersets. Neither is a Liouville number. Also, every real number can...

...either operation. Transcendental numbers? The paper cites this theorem: if x and y are transcendental numbers, then at least one of x + y and x*y is transcendental. Proof: let x + y = a and x*y = b and solve for x and y: x = (1/2)*(a - sqrt(a^2 - 4*b)) y = (1/2)*(a + sqrt(a^2 - 4*b)) and...

Yes, as early CPU chips. But they were one-off designs, not members of instruction-set-compatible families.

Liouville number - a kind of transcendental number. It is a real number x with the property that for every positive integer n, there is some p and q that satisfy \displaystyle{ 0 < \left| x - \frac{p}{q} \right| < \frac{1}{q^n} } That means that Liouville numbers are almost rational numbers...

I'll use LaTeX on the gamma-function content of one of my earlier posts. \Gamma(1) = 1 ,\ \Gamma(\frac12) = \sqrt{\pi} Transcendental and algebraically independent of pi: \Gamma(\frac16) , \Gamma(\frac14) ,\ \Gamma(\frac13) ,\ \Gamma(\frac23) ,\ \Gamma(\frac34) ,\ \Gamma(\frac56)...

Fighting for Reproductive Freedom | Alexandria Ocasio-Cortez - YouTube - at Las Vegas NV Great speech. On the podium: "Biden-Harris: Fighting for Reproductive Freedom" She described how she is a "Planned Parenthood baby", and how her mother chose to have her, and she then described what she...

Turning to three more of the 10C's, Exodus 20:7 KJV: Thou shalt not take the name of the LORD thy God in vain; for the LORD will not hold him guiltless that taketh his name in vain. "Take in vain" is not very obvious to Modern-English speakers, and some translations instead use "misuse"or...

Seems like the third partiers that I run into online. They seem to think that the Presidential election is the only election worth considering and they seem ignorant of Duverger's law. Consider the US Green Party. It seems like a Presidency-only party with other offices an afterthought. Some...

That "unified Reich" was the Second Reich, the late 19th cy. German Empire, not the Third Reich. The First Reich was the Holy Roman Empire, a loose confederation that was none of these things.

This desert moss has the potential to grow on Mars | ScienceDaily Refers to that paper: Tingyun Kuang, Yuanming Zhang, Daoyuan Zhang. The extremotolerant desert moss Syntrichia caninervis is a promising pioneer plant for colonizing extraterrestrial environments. The Innovation, 2024; 100657...

How are the languages related? I'll start off with Indo-European. Germanic West Germanic: English, Dutch, German North Germanic: Norwegian Celtic: Gaelic, Welsh Italic: Latin Greek Indo-Iranian: Sanskrit Semitic: West Semitic: Central Semitic Northwest Semitic Aramaic Canaanite: Punic...

I like Roosevelt: "rose field" or "field of roses" in Dutch. The "velt" part is cognate to English "field", from Proto-Germanic *felthuz likely from Proto-Indo-European *pletH- "flat" inferred from Latin plânus "flat" and Greek platu- "flat" and English "flat" itself. The "roose" part is from...

Though she is not yet a President and may never be, Kamala Harris has a very unusual first name by President standards, though her last name is much more typical. So I decided to research the names of US Presidents and Vice Presidents with the help of The Meaning and History of First Names -...

It will still need liquid-water temperature and pressure to grow, however, and only a little bit of Mars's surface can have liquid water, and only for a little bit of the time. From the article, It needs "normal growth conditions" to grow - what are the researchers calling "normal"? There is...

Opinion | Joe Biden Is a Good Man and a Good President. He Must Bow Out of the Race. - The New York Times Could Democrats Replace Biden at the Top of the Presidential Ticket? - The New York Times - "While it is possible, it would most likely lead to political upheaval in the party unless the...