89. Living out justice in the Church means purifying ecclesial relationships and structures from distortions that give rise to inequality, lack of transparency and abuse of power. In this regard, listening to the victims of spiritual, economic, institutional, sexual and power-based abuse, as well as abuses of conscience, is an integral part of a journey toward justice, which includes acknowledging the harm done, just reparation and taking steps to prevent it from happening again. Every power is at the service of communion and mission. All authority is at the service of the People of God. This ministry of service is expressed not only through our faith celebrated and lived in the Sacraments, and in the adoption of a synodal style, but also in the concrete sharing of goods. Following the example of the early Church, ecclesial resources need to be shared so that no one among us may be in need (cf. Acts 434, and so that their administration may support the mission of proclaiming the Gospel to the poorest. Regular assessments of the exercise of ministerial responsibilities should be encouraged, not as judgments on individuals, but as tools for learning and correction oriented toward mission. 116 Only to the extent that we are open to the action of the Holy Spirit will these principles of Social Doctrine become incarnate in ecclesial life. In this way, the Church will be able to bear credible witness to society that seeking the common good together, with shared responsibility and fraternity, is not a utopia, but a real possibility.
I did read it, but words are cheap, even very flowery words that make all sorts of promises. There's no particular reason to trust that organization's leadership, so any promises should be believed only once results materialize and last for some period of time. I for example would hesitate to credit the church with stamping out abuse just because no major stories have broken this year (that I'm aware of).
Likewise when it comes to changing their practical stances and teaching on matters that have very real impacts on health and wellbeing of so many, I'll believe it when I see the results for some time.
There have been bills in the past like "The improved digital identity act of 2023" that never get out of committee. The latest incarnation seems to be "H.R.7270 - Stop Identity Fraud and Identity Theft Act of 2026". There almost always have one republican and one democratic sponsor. But they don't seem to rise to the level of urgency to get past the current dysfunction in congress.
I was trying to understand how this could be used for flights. I've seen either having to enter your last name and seat, or loyalty plan number to get in-flight wifi. Are there really airline wifis that give every mac address a free amount of time?
A lot of airlines now offer free "messaging" - usually just text on common messaging apps like WhatsApp. I've been meaning for years to write some kind of server that could give me useful functionality over chat messages.
Pretty sure it will work on JAL at least right now. They just asked for an email. But it was also a new service so maybe to wanted people to try it. It occurred to me at the time that two devices with two emails should work for twice as long. For what I wanted to do on that flight, i.e. check and send a few messages the one free hour was fine. But yeah of course they could change it so that would not work.
You can run the model for free on openrouter.ai. I have played around with lean, slowly working my way through mathmatics in lean. I was stuck on this problem in section 3.6
theorem convergesTo_unique {s : ℕ → ℝ} {a b : ℝ}
(sa : ConvergesTo s a) (sb : ConvergesTo s b) :
For fun I tried it on the free model on openrouter.ai. Got the answer the first time.
by_contra h
have h₁ : a ≠ b := h
have h₂ : |a - b| > 0 := by
apply abs_pos.mpr
exact sub_ne_zero.mpr h₁
-- Use the definition of convergence to find N₁ and N₂
have h₃ := sa (|a - b| / 2) (by linarith)
have h₄ := sb (|a - b| / 2) (by linarith)
cases' h₃ with N₁ h₃
cases' h₄ with N₂ h₄
-- Choose N to be the maximum of N₁ and N₂
let N := max N₁ N₂
have h₅ := h₃ N (by simp [N, le_max_left])
have h₆ := h₄ N (by simp [N, le_max_right])
-- Derive a contradiction using the triangle inequality
have h₇ : |s N - a| < |a - b| / 2 := by simpa using h₅
have h₈ : |s N - b| < |a - b| / 2 := by simpa using h₆
have h₉ : |a - b| < |a - b| := by
calc
|a - b| = |a - s N + (s N - b)| := by ring_nf
_ ≤ |a - s N| + |s N - b| := by
apply abs_add
_ = |s N - a| + |s N - b| := by
rw [abs_sub_comm]
_ < |a - b| / 2 + |a - b| / 2 := by
linarith
_ = |a - b| := by ring
linarith
https://m.youtube.com/watch?v=J5Sb21qbpEQ
reply