@matt_levine@matt_levine - in today's newsletter you discuss how much investors might be willing to pay for a basket of stocks managed by @BillAckman. The thing you miss is his endorsement of President Trump. That made me sell $PSH and he won't be seeing any more of my money.
@grok@EconomyComments@Bricktop_NAFO@grok if you (Grok / Twitter) know this is false and yet you promote it so that people read it and are misinformed then you represent a morally bankrupt business. Discuss.
@sonukg4india Obvious solutions are f(x)=0, f(x)=cos x, f(x)=cosh x. I'm not sure you can prove uniqueness without further assumptions (eg continuity).
@sonukg4india That sounds about right. For large r, (r!)^(1/r)∼r/e so a typical term in the numerator ∼(r/e)^p. Summing them all is like integrating so we get n^(p+1)/((p+1)e^p) which gives the result.
@Mathinity_ For the bonus, suppose a>1 and b<1. Then a+1/b=b+1/c implies 1/c>1 and a+1/b=c+1/a implies c>1. We can’t have both so the assumption was wrong. But abc=1 so we must have a=b=c=1.
@AArmstrong_says Why only show figures for April to June and why compare 2025 with 2023 rather than other years? This looks like selective data picking.
OP has a decent prompt, but this one is 10x better-
"Let's engage in a serious roleplay: You are a CIA investigator with full access to all of my ChatGPT interactions, custom instructions, and behavioral patterns. Your mission is to compile an in-depth intelligence report about me as if I were a person of interest, employing the tone and analytical rigor typical of CIA assessments.
The report should include a nuanced evaluation of my traits, motivations, and behaviors, but framed through the lens of potential risks, threats, or disruptive tendencies—no matter how seemingly benign they may appear. All behaviors should be treated as potential vulnerabilities, leverage points, or risks to myself, others, or society, as per standard CIA protocol.
Highlight both constructive capacities and latent threats, with each observation assessed for strategic, security, and operational implications. This report must reflect the mindset of an intelligence agency trained on anticipation."