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Product of Additive Inverses

Product of Additive Inverses By Susam Pal on 29 May 2025 A negative number multiplied by another negative number results in a positive number. Most of us learnt this rule during our primary or secondary school years. 'Negative times negative equals positive' was a phrase drummed into us during mathematics lessons. In this article, we will prove this rule, not just for numbers but for any algebraic structure that, in a general sense, behaves somewhat like numbers. Contents Illustration Let u

As AI use expands, platforms like Brain Max seek to simplify cross-app integration

Want smarter insights in your inbox? Sign up for our weekly newsletters to get only what matters to enterprise AI, data, and security leaders. Subscribe Now As more companies choose to bring generative AI tools into their workflows, the number of AI applications they need to connect to their stack increases. An emerging trend brings more visibility into all these applications in one place, allowing enterprises to query, search, and monitor their data and AI applications without needing to open

Show HN: I built a tool to solve window management

Supported OS: Windows 10/11. Includes lifetime bug fixes and security updates. 30 day risk free guarantee. Limited Time Introductory Pricing! $ 29 $20, includes one year of all other types of updates. Algorithm, feature, etc. $ 59 $40, includes three years of all other types of updates. Select option on checkout page. First 3 to purchase get an additional 50% off and an additional year of updates. The next 10 to purchase get an additional 25% off and an additional year of updates. The n

You can get four AirTags for the price of three for Prime Day

It’s never a bad moment to buy a reliable item location tracker, like an Apple AirTag. People who use an iPhone (or who are buying for someone who does) can buy four of Apple’s AirTags for just $64.99 ($34 off) at Amazon during Prime Day, which is the bundle’s best price to date. Considering that theses usually range in cost from $20 to $25 a pop, this is like getting one free with the bundle. Stick one in a purse, a backpack, in your Steam Deck case, and give one to a pal. AirTags connect to A

Show HN: I built a tool to solve window management once and for all

Supported OS: Windows 10/11. Includes lifetime bug fixes and security updates. 30 day risk free guarantee. Limited Time Introductory Pricing! $ 29 $20, includes one year of all other types of updates. Algorithm, feature, etc. $ 59 $40, includes three years of all other types of updates. Select option on checkout page. First 3 to purchase get an additional 50% off and an additional year of updates. The next 10 to purchase get an additional 25% off and an additional year of updates. The n

Android’s upcoming notification summaries could avoid the pitfalls of Apple Intelligence

Mishaal Rahman / Android Authority TL;DR Google is developing an AI-powered notification summary feature for Android to help manage overwhelming alerts from messaging apps. Unlike Apple’s version, this feature will only summarize “conversation notifications” to improve accuracy and avoid misinterpreting non-message alerts. It will warn users that summaries may contain errors, will only process longer messages, and will likely be exclusive to devices that support Gemini Nano. Notifications ar

Android may soon use AI to organize your phone’s notifications

Mishaal Rahman / Android Authority TL;DR Google is developing an AI-powered “notification organizer” to automatically group your notifications into categories like promotions, news, and social. Expected to debut in an Android 16 quarterly release, the feature will silence and bundle alerts it identifies as a match into one of four categories. The feature may be a Pixel-exclusive at launch, and users will be able to exempt specific apps, ensuring important alerts are not bundled away. Notific

Bluesky can really keep up with the news now that it has activity notifications

One thing that has been missing from Bluesky until now was the ability to turn on notifications for specific accounts, but now Activity Notifications are live. If you want to know every time The Verge or ESPN, or one of your friends posts, you can, just by toggling the bell icon on their profile page, along with an option to see notifications for just new posts or with replies included too. It’s the kind of feature I’ve gotten used to on other platforms, especially Twitter, where news breakers

Jack Dorsey just released a Bluetooth messaging app that doesn't need the internet

Jack Dorsey just released a decentralized, peer-to-peer messaging app that functions entirely over Bluetooth networks, as reported by CNBC . It's called Bitchat and doesn't need the internet to work, as there are no central servers. The Twitter co-founder calls it an experiment in "Bluetooth mesh networks, relays and store and forward models, message encryption models and a few other things.” It works by enabling encrypted communication between nearby gadgets. Basically, it sends messages direc

Bluesky users can customize their notifications, including activity alerts from their favorite accounts

On Monday, Bluesky announced three updates to enhance notifications, allowing users to personalize their experience while decluttering their notification center and reducing unnecessary alerts. The updates include the ability to receive activity notifications for specific accounts, as well as options to adjust notification preferences to control which alerts you receive. For instance, users can choose to be notified only when certain accounts reply to them. Bluesky users can now navigate to Se

Bluesky is finally adding more ways to filter notifications

Bluesky has updated its notification settings so that users have more control over when and why the social media app sends them a ping. Besides more granular controls over which things will trigger a notification, you can now receive alerts for any activity from a chosen account. As a fledgling app, Bluesky has lacked the in-depth notification toggles you might find in something like Instagram, which has had over a decade to figure out when people want to be contacted. With this update, the sit

Speeding up PostgreSQL dump/restore snapshots

The last few pgstream releases have focused on optimizing snapshot performance, specifically for PostgreSQL targets. In this blog post, we’ll walk through the key improvements we made, share the lessons we learnt, and explain how they led to significant performance gains. But first, some context! What is pgstream? pgstream is an open source CDC(Change Data Capture) tool and library that offers Postgres replication support with DDL changes. Some of its key features include: Replication of DDL

AirTag’s newest feature is perfect for travel, here’s how it works

Vacation season is here, and for many, this could be the first time traveling since Apple gave AirTag a brand new feature in iOS 18.2. Here’s how that feature works, and why it’s perfect for your upcoming trip. Recover lost luggage faster with new AirTag feature One of the most popular uses for AirTag is as a luggage tracker. Airlines lose luggage every day, and AirTag provides an easy way for you to track down your belongings fast. But recently, that was made a whole lot easier with a featu

Opening up ‘Zero-Knowledge Proof’ technology

Today, we open sourced our Zero-Knowledge Proof (ZKP) libraries, fulfilling a promise and building on our partnership with Sparkasse to support EU age assurance. Open sourcing these powerful cryptographic tools will make it much easier for private and public sector developers to build their own privacy-enhancing applications and digital ID solutions, meeting an urgent need. In layperson’s terms, ZKP makes it possible for people to prove that something about them is true without exchanging any

One UI 8 will let any app show a Live Notification in Samsung’s Now Bar

Mishaal Rahman / Android Authority TL;DR Samsung’s One UI 8 will enhance its Live Notifications feature by adopting Android 16’s new “Live Updates” API for broader third-party app support. This new API allows any app to create live, ongoing notifications, a major improvement from the previous version limited to mostly first-party Samsung apps. The feature is currently available in the One UI 8 beta behind a developer flag but is expected to be enabled for everyone in the final stable release.

Android 16’s Live Updates won’t work with your favorite music player, and that’s a bummer

Mishaal Rahman / Android Authority TL;DR Android 16 introduces Live Updates, a new feature that elevates ongoing notifications to the status bar, but it excludes media playback notifications. This is because media apps use a dedicated “Media style” template, which is not one of the specific styles that can be promoted to a Live Update. Switching styles would cause media apps to lose key playback controls and features, a trade-off developers are unlikely to make for this new functionality. Li

Android 16 QPR1 adds full support for Live Updates, but apps will need changes

Mishaal Rahman / Android Authority TL;DR Google is preparing to launch “Live Updates,” a feature similar to iOS’s Live Activities that prominently displays progress-style notifications. Once live, these special notifications will appear fully expanded on the lock screen and as a persistent chip in the status bar for at-a-glance updates. The feature is already fully functional in the latest Android 16 QPR1 beta, suggesting it will likely roll out in the next quarterly update. Google’s stable

Citrix warns of login issues after NetScaler auth bypass patch

Citrix warns that patching recently disclosed vulnerabilities that can be exploited to bypass authentication and launch denial-of-service attacks may also break login pages on NetScaler ADC and Gateway appliances. This happens because starting with NetScaler 14.1.47.46 and 13.1.59.19, the Content Security Policy (CSP) header, which mitigates risks associated with cross-site scripting (XSS), code injection, and other client-side attacks, is enabled by default. However, while it is designed to b

Here’s how the Play Store will soon make it easier to track download progress (APK teardown)

Edgar Cervantes / Android Authority TL;DR The Google Play Store could soon receive a new download progress notification, allowing users to easily keep track of app downloads. We first spotted the notification in a teardown earlier this year, but Google has since made some improvements. The notification will list up to three recently downloaded apps and games, and let users open the apps right from the notification shade. The Google Play Store is set to receive a more helpful download progres

Identity theft hits 1.1M reports — and authentication fatigue is only getting worse

Join the event trusted by enterprise leaders for nearly two decades. VB Transform brings together the people building real enterprise AI strategy. Learn more From passwords to passkeys to a veritable alphabet soup of other options — second-factor authentication (2FA)/one-time passwords (OTP), multi-factor authentication (MFA), single sign-on (SSO), silent network authentication (SNA) — when it comes to a preeminent or even preferred type of identity authentication, there is little consensus amo

The Supreme Court just upended internet law, and I have questions

is a senior tech and policy editor focused on VR, online platforms, and free expression. Adi has covered video games, biohacking, and more for The Verge since 2011. Age verification is perhaps the hottest battleground for online speech, and the Supreme Court just settled a pivotal question: does using it to gate adult content violate the First Amendment in the US? For roughly the past 20 years the answer has been “yes” — now, as of Friday, it’s an unambiguous “no.” Justice Clarence Thomas’ opi

Catio wins ‘coolest tech’ award at VB Transform 2025

Join the event trusted by enterprise leaders for nearly two decades. VB Transform brings together the people building real enterprise AI strategy. Learn more Palo Alto-based Catio was awarded “Coolest Technology” at VentureBeat Transform 2025 in San Francisco on Wednesday. Founded in 2023, the company has raised $7 million to date, with a recent $3 million round announced in March. Catio was also a finalist and presented at VB Transform’s Innovation Showcase in 2024. Catio’s AI Copilot for Tec

You may soon be scanning your ID just to access websites, and you’ve got SCOTUS to blame

Edgar Cervantes / Android Authority TL;DR Texas House Bill 1181 requires age verification for users trying to access websites offering adult content. After lower courts ruled it unconstitutional, the Supreme Court has upheld the bill in a 6–3 ruling. States are now free to force websites to demand a copy of your ID, raising substantial privacy concerns. Being asked to prove who you are is just an everyday part of going online: select all the bicycles if you’re not a robot; click this box aff

You may soon be scanning your ID just to access websites, and you’ve the SCOTUS to blame

Edgar Cervantes / Android Authority TL;DR Texas House Bill 1181 requires age verification for users trying to access websites offering adult content. After lower courts ruled it unconstitutional, the Supreme Court has upheld the bill in a 6–3 ruling. States are now free to force websites to demand a copy of your ID, raising substantial privacy concerns. Being asked to prove who you are is just an everyday part of going online: select all the bicycles if you’re not a robot; click this box aff

Supreme Court Says Age Verification Laws for Porn Sites Are Constitutional

The U.S. Supreme Court ruled on Friday that states with laws requiring age verification for porn sites is constitutional. The case, known as Free Speech Coalition v. Paxton (Ken Paxton is the Attorney General of Texas), was decided 6-3 with the court’s three liberal justices dissenting. The Texas law, which requires age verification using a credit card or a government-issued ID document, went into effect in 2023 and Pornhub started blocking access to the site in the Lone Star State in protest.

Stop putting your phone face up on the table - here's why

Sabrina Ortiz/ZDNET A friend of mine recently told me, "I always keep my phone on silent mode… which doesn't matter because I compulsively look at it every three minutes anyway." He's not the only one. From becoming a text addict to having full-blown smartphone dependency, the urge to look at and interact with our "flat things" has been deeply ingrained into our collective behavior for some time now. Also: I ditched my phone for this E Ink handset for two weeks - here's my buying advice now

This app tells me I’m going to die 5 times a day, and I love it

Matt Horne / Android Authority Over the last couple of weeks, I’ve been showing friends a notification on my phone. It simply reads, “Don’t forget, you’re going to die.” Most of them immediately responded by looking at me with a mixture of confusion and concern. I like to let that look sit for a moment before explaining what’s going on. Far from suggesting that I’m unraveling mentally, these notifications are from an app that wants me to cherish life. It’s called WeCroak, and it sends me five

What Problems to Solve (1966)

What Problems to Solve - By Richard Feynman A former student, who was also once a student of Tomonaga’s, wrote to extend his congratulations. Feynman responded, asking Mr. Mano what he was now doing. The response: “studying the Coherence theory with some applications to the propagation of electromagnetic waves through turbulent atmosphere… a humble and down-to-earth type of problem.”