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Product of Additive Inverses

news.ycombinator.com Unknown 2025-10-08 23:50:38

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

Topics: additive cdot multiplication ring times

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Watch Robert Downey Jr. Geek Out About ‘Ironheart’ for 14 Minutes

gizmodo.com Germain Lussier 2025-10-12 12:00:08

It’s still unclear what impact, if any, the events of Ironheart will have on the future of the Marvel Cinematic Universe, but at least one person in it has already felt the effects. That would be Robert Downey Jr., the former Tony Stark, current Victor Von Doom and basically the Godfather of the MCU. Downey is a busy man, but he still found time to sit down with Ironheart star Dominique Thorne to geek out about the show for 14 minutes, and it’s just a delight. In what’s apparently just part one

Topics: downey ironheart just mcu thorne

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Fitbit Charge 6 Fitness Tracker Is Going for Peanuts With Prime Discount, Includes S and L Sized Bands

gizmodo.com Jason Coles 2025-10-12 12:10:05

It’s not just bits and bobs for the house you can pick up during this month’s Prime Day deal event, it’s basically everything. If there’s anything that Amazon sells that you’d like to save money on, then this event means there’s a high chance that you’ll be able to do so. It’s a good chance to get tech that you’d normally skip over because of its price. There are big deals all over the place. One great deal we’ve found today is on the immensely useful Fitbit Charge 6 fitness tracker. This handy

Topics: chance deal health just sure

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If You Don’t Have One Yet, This Blueair Air Purifier for XL Rooms Is Flying Off the Shelves on Prime Day

gizmodo.com Gizmodo Deals 2025-10-12 12:15:49

Indoor pollution management is a headache by itself, and it’s a situation that can lead to serious health problems unless tackled in the long term. In order to keep your home air clean and your mind at peace, luxury brands such as Dyson and Blueair make available the best air purifiers. While Dyson is trendy and among Prime Day deals, Blueair is a niche player in the air purifier space and its Blue Pure 211i Max model is specifically designed for bigger rooms. This Prime Day, Amazon’s sale pric

Topics: air amazon blue blueair day

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Microsoft Surface Laptop (16GB RAM, 512GB SSD) Hits a Price That Makes Old Tags Look Silly Thanks to Prime Day

gizmodo.com Joe Tilleli 2025-10-12 12:25:36

Happy Prime Day to all who celebrate. This week you can all sorts of excellent deals across every product category at Amazon from laptops to treadmills to food processors to other laptops. If that happens to be exactly what you’re in the market for, you should pay attention to this Microsoft Surface deal. This 2024 touchscreen laptop is part of this week of savings and you can chop off 34% from the price. It’s normally $1,200, but for a limited time you can grab it for just $790. That’s bring it

Topics: day laptop microsoft surface usb

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Amazon Moves Fast, Roborock Qrevo S5V Is 40% Off Barely a Week After Hitting the Market

gizmodo.com Gizmodo Deals 2025-10-12 12:40:22

Roborock has become the most premium brand out there in the robot vacuum market with premium models like the Saros Series that fetch over $1,500. The company also does a great job of offering edge-of-the-time technology at a more affordable price for the masses: That’s exactly what you’ll experience with the new Qrevo S5V which just landed in stores and is available today in an incredible Prime Day bargain. Just a week after its release, Amazon is marking down this model 40% for Prime shoppers,

Topics: avoid qrevo s5v suction time

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The Phantom of the Opera Has a Lot of Demands for His Immersive Masquerade

gizmodo.com Sabina Graves 2025-10-12 12:45:37

The mystery of Masquerade, The Phantom of the Opera immersive Broadway experience, begins to unfold as tickets for the initial run announcement have sold out. Don’t worry, Andrew Lloyd Webber “phans,” on July 9 there will be a new drop of tickets for an extension going into October of this year. Perfect for spooky season monster haunt lovers, dare we say? Hey, dark musical fans and immersive haunt goers have a very real overlap! With the release of the Opera Ghost’s first batch of show dates, t

Topics: experience immersive masquerade opera phantom

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Prime Day Shopping: How to Get the Deals Without Getting Scammed

cnet.com See Full Bio 2025-10-12 10:51:00

Amazon's Prime Day sale is officially here, but shoppers looking for great deals need to be careful that they don't get scammed in the process. Amazon is warning consumers to be on the lookout for cybercriminals attempting to use the massive online event, which runs Tuesday through Friday, as an opportunity to con them out of their money and personal information. According to Amazon, reports of email impersonation scams, where cybercriminals tried to pass themselves off as Amazon or another re

Topics: amazon check day prime scam

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Grab Prime Day Laptop Savings: My Go-to Acer Aspire 14 AI Is Nearly 30% Off at Costco Right Now

cnet.com See Full Bio 2025-10-12 10:59:00

Amazon's Prime Day may have started July 8, but other retailers are offering some major discounts as well. Costco members can snag the Acer Aspire 14 AI for $500a $200 discount, until July 20 or while supplies last. CNET's key takeaways The Acer Aspire 14 AI is available for $500 at Costco. The Intel Lunar Lake CPU offers good performance for the price and long battery life. The display and design won't wow you. Laptop prices are on the rise -- and the more they increase, the better Acer's

Topics: 14 ai aspire budget laptop

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Today's NYT Strands Hints, Answers and Help for July 9 #493

cnet.com See Full Bio 2025-10-12 11:00:04

Looking for the most recent Strands answer? Click here for our daily Strands hints, as well as our daily answers and hints for The New York Times Mini Crossword, Wordle, Connections and Connections: Sports Edition puzzles. Today's NYT Strands puzzle is a fun topic, but some of the words get a little long to unscramble. If you need hints and answers, read on. I go into depth about the rules for Strands in this story. If you're looking for today's Wordle, Connections and Mini Crossword answers,

Topics: hints puzzle strands today words

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Today's NYT Connections Hints, Answers and Help for July 9, #759

cnet.com See Full Bio 2025-10-12 11:00:05

Looking for the most recent Connections answers? Click here for today's Connections hints, as well as our daily answers and hints for The New York Times Mini Crossword, Wordle, Connections: Sports Edition and Strands puzzles. Today's NYT Connections puzzle has another of those classic purple categories today, where you have to somehow recognize a part of four words and make a connection among them that way. Read on for clues and today's Connections answers. The Times now has a Connections Bot,

Topics: answers connections group today words

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Today's NYT Connections: Sports Edition Hints and Answers for July 9, #289

cnet.com See Full Bio 2025-10-12 11:00:07

Looking for the most recent regular Connections answers? Click here for today's Connections hints, as well as our daily answers and hints for The New York Times Mini Crossword, Wordle and Strands puzzles. Basketball fans might get a slam dunk with the tougher categories in today's Connections: Sports Edition. There's a playful twist on tap for the purple group, so think creatively. Read on for hints and the answers. Connections: Sports Edition is out of beta now, making its debut on Super Bowl

Topics: answers connections group sports today

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Best Vacuum for Hardwood Floors in 2025

cnet.com See Full Bio 2025-10-12 11:20:00

Roomba J7 Plus (Out of stock): Roomba may still be the most recognized name in robot vacuums, and that's not only because it was a pioneer in the space, but because it continues to make very good robot vacuums. The Roomba J7 Plus may not be the newest model on the block from iRobot, but it still offers solid performance. During our lab tests, the Roomba J7 Plus swept up all the sand in our hardwood floor testing. It also does so efficiently with its RGB camera and 3D sensor for navigation and ob

Topics: hardwood j7 robot roomba sand

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Best Cheap Vacuums for 2025: Our Best Lab-Tested Performers for Less Than $300

cnet.com See Full Bio 2025-10-12 11:24:00

Dyson Dyson V8 Absolute: The V8 Absolute is one of the more affordable Dyson vacuums you can buy. Normally $520 at full price, it's currently on sale for $350. That still makes it more expensive than most of the vacuums on this list. In testing, it did great on hardwood, removing nearly 98% of sand, but it didn't do as hot on carpet. The Absolute was able to remove 68.3% of sand from low-pile and 52% from midpile, falling short of many competitors, including the Levoit LVAC-200 and Shark Strato

Topics: hardwood low performance pile sand

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It's Nearly Time for Samsung's Galaxy Z Fold 7 and Z Flip 7 Debut: How to Watch the Unpacked Event

cnet.com See Full Bio 2025-10-12 11:45:00

Samsung's Unpacked event may just introduce the next generation of foldable Galaxy Z phones to replace the Galaxy Z Fold 6 and Galaxy Z Flip 6 (if the company's multiple teases are to be believed). Samsung is also expected to unveil the successor to the Galaxy Watch 7. The event happens tomorrow. Here's what you can expect and how to tune in. CNET is also hosting a Samsung Galaxy Unpacked live blog and a live show, which will cover all the final rumors and big reveals as they happen. When is Sa

Topics: fold galaxy samsung unpacked watch

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8 Best Amazon Prime Day Vacuum Deals for Dust and Dirt in 2025

wired.com Nena Farrell 2025-10-12 12:15:41

Cleaning isn't just for spring, and these Amazon Prime Day vacuum deals are ones you can't miss if you're looking for a better vacuum. The insanity of summer—beach days! sunscreen spills! sticky ice cream!—leaves me cleaning more often than I was in the springtime or any other season. A great vacuum makes a huge difference. Whether I'm grabbing my favorite stick vacuum for the stairs, a car vacuum for my Sisyphean car mess, or a Dyson to solve all my problems, you can usually find me with a vacu

Topics: best dyson robot stick vacuum

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From Point Clouds to Photorealism: How PRoGS Advances the State of Neural Rendering

computer.org Enrique Quezada 2025-10-12 15:34:42

What if a real-time automated decision-making process needs a computer vision system to produce photorealistic visuals in a mere fraction of a second? In many cases, this requires too much computational power — if it’s even possible at all. When computer vision uses 3D Gaussian splatting (3DGS), it provides a photorealistic image, but the process takes far too long. For more on this topic, see our article on computer vision for disaster responses. This article discusses a new approach, Progress

Topics: image progs rendering republic splats

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Elon Musk lashes out at Tesla bull Dan Ives over board proposals: 'Shut up'

cnbc.com Lora Kolodny 2025-10-12 14:35:24

Elon Musk, chief executive officer of SpaceX and Tesla, attends the Viva Technology conference at the Porte de Versailles exhibition center in Paris, June 16, 2023. Tesla CEO Elon Musk told Wedbush Securities' Dan Ives to "Shut up" on Tuesday after the analyst offered three recommendations to the electric vehicle company's board in a post on X. Ives has been one of the most bullish Tesla observers on Wall Street. With a $500 price target on the stock, he has the highest projection of any analy

Topics: board ceo ives musk tesla

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Apple says COO Jeff Williams will retire from company later this year

cnbc.com Kif Leswing 2025-10-12 16:59:40

Jeff Williams, chief operating officer of Apple Inc., during the Apple Worldwide Developers Conference (WWDC) at Apple Park campus in Cupertino, California, US, on Monday, June 9, 2025. Apple said on Tuesday that Chief Operating Officer Jeff Williams, a 27-year company veteran, will be retiring later this year. Current operations leader Sabih Khan will take over much of the COO role later this month, Apple said in a press release. For his remaining time with the comapny, Williams will continue

Topics: apple cook said team williams

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A Fast-Rising Gaming YouTuber Is an AI Construct, Not a Human

futurism.com Unknown 2025-10-12 15:44:49

With 2.57 million subscribers and more than 800 million views, a YouTuber named Bloo is swiftly becoming one of the biggest gaming personalities in the biz. But unlike his human peers, this blue-haired vlogger is a cartoonish AI-powered avatar — perhaps the clearest sign yet of AI's deep and industry-shaking inroads into the world of entertainment and influencers. In an interview with CNBC, Bloo's creator, Dutch YouTuber and AI enthusiast Jordi van den Bussche, said that he decided to unleash

Topics: ai avatar bloo den van

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OpenAI May Be in Major Trouble Financially

futurism.com Unknown 2025-10-12 16:20:01

Since OpenAI unleashed ChatGPT on the world two and a half years ago, the company has operated at a substantial financial loss. Despite raising at least $60.9 billion in private funding since ChatGPT's public launch, OpenAI is leaking billions of dollars every year. In 2024, for example, the tech startup lost some $5 billion, per MSNBC. That doesn't seem to bother OpenAI insiders, though, who hope to be bringing in $125 billion in annual revenue by 2029. The gulf between OpenAI's ambitions and

Topics: ai anthropic hikes openai zitron

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

venturebeat.com Emilia David 2025-10-12 15:03:27

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

Topics: applications brain clickup max said

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Prime Day pick: Save a record 33% on the Sonos Ace headphones

androidauthority.com Unknown 2025-10-12 16:30:03

Audiophiles, listen up — there’s a fantastic deal on the Sonos Ace headphones that’s perfect for enhancing your listening experience. Right now, you can grab the Sonos Ace for just $299, a significant drop from its usual price of $449. That’s a 33% discount, and it brings the headphones to their lowest price of all time. Sonos Ace Headphones for $299 (33% off) These headphones pack several impressive features. With plush vegan leather ear cushions and a stainless steel headband, the Sonos Ace p

Topics: ace deal headphones prime sonos

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Aqara HomeKit smart locks, cameras, and more offer Prime Day discounts of up to 38%

9to5mac.com Sponsored Post 2025-10-12 16:30:00

9to5Mac readers know the value of HomeKit compatibility when it comes to smart locks, security cameras, and other devices – and Aqara’s extensive product range has you covered. There’s never been a better time to buy, thanks to Amazon Prime Day discounts of up to 38% on some of the company’s most popular products … Smart Lock U100 A smart lock is one of the biggest upgrades you can give to your home, boosting security while also offering a whole new level of convenience and flexibility. The

Topics: 99 aqara camera home smart

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Apple COO Jeff Williams stepping down later this month

9to5mac.com Chance Miller 2025-10-12 16:34:25

Apple has announced that Jeff Williams is stepping down as chief operating officer later this month. Sabih Khan, Apple’s senior vice president of Operations, will assume the COO role as part of what Apple describes as a “long-planned succession.” Williams joined Apple in 1998 as the company’s head of Worldwide Procurement. Prior to joining Apple, he worked at IBM for thirteen years across multiple operations and engineering roles. In his current role at Apple, he oversees the company’s entire w

Topics: apple operations tim williams years

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You can (finally) buy the Nintendo Switch 2 on Amazon now (but don't expect a Prime Day deal)

engadget.com Unknown 2025-10-12 15:55:58

Engadget has been testing and reviewing consumer tech since 2004. Our stories may include affiliate links; if you buy something through a link, we may earn a commission. Read more about how we evaluate products . The scramble to buy the first wave of Nintendo Switch 2 gaming consoles left a lot of fans in the lurch. Getting your hands on a Switch 2 of your own still takes some luck if you weren't fortunate enough to snag a pre-order. One of the points of drama has been that major seller Amazon

Topics: amazon buy buying invite switch

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M&S confirms social engineering led to massive ransomware attack

bleepingcomputer.com Unknown 2025-10-12 16:39:53

M&S confirmed today that the retail outlet's network was initially breached in a "sophisticated impersonation attack" that ultimately led to a DragonForce ransomware attack. M&S chairman Archie Norman revealed this in a hearing with the UK Parliament's Business and Trade Sub-Committee on Economic Security regarding the recent attacks on the retail sector in the country. While Norman did not go into details, he stated that the threat actors impersonated one of the 50,000 people working with the

Topics: actors attack dragonforce ransomware threat

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Samsung announces major security enhancements coming to One UI 8

bleepingcomputer.com Unknown 2025-10-12 16:43:04

Samsung has announced multiple data security and privacy enhancements for its upcoming Galaxy smartphones running One UI 8, its custom user interface on top of Android. Key highlights include the introduction of a system-level architecture named Knox Enhanced Encrypted Protection (KEEP), upgrades to Knox Matrix, and the addition of quantum resistance to WiFi connectivity. Keeping AI data secure With AI tools taking an increasing role in day-to-day smartphone use, protecting user inputs has be

Topics: data galaxy knox matrix samsung

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The 25 best Prime Day 2025 deals under $25

zdnet.com Allison Murray 2025-10-12 15:55:00

'ZDNET Recommends': What exactly does it mean? ZDNET's recommendations are based on many hours of testing, research, and comparison shopping. We gather data from the best available sources, including vendor and retailer listings as well as other relevant and independent reviews sites. And we pore over customer reviews to find out what matters to real people who already own and use the products and services we’re assessing. When you click through from our site to a retailer and buy a product or

Topics: content does editorial reviews zdnet

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5 surprise products Samsung may unveil at Unpacked tomorrow - including a tri-foldable phone

zdnet.com Cesar Cadenas 2025-10-12 16:03:00

Kerry Wan/ZDNET It's hard to believe that we're already halfway through 2025, and Samsung is kicking off the second half with force. The tech giant will hold its next Unpacked event tomorrow, Wednesday, July 9, at 10 a.m. EST. Officially, we know very little about what will be shown on the big day, but that isn't to say that teaser information doesn't exist. Ever since the last Unpacked event back in January, several leaks and rumors have cropped up online, providing a view into what could be

Topics: device event galaxy information samsung

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Latest Tech News

Product of Additive Inverses

Watch Robert Downey Jr. Geek Out About ‘Ironheart’ for 14 Minutes

Fitbit Charge 6 Fitness Tracker Is Going for Peanuts With Prime Discount, Includes S and L Sized Bands

If You Don’t Have One Yet, This Blueair Air Purifier for XL Rooms Is Flying Off the Shelves on Prime Day

Microsoft Surface Laptop (16GB RAM, 512GB SSD) Hits a Price That Makes Old Tags Look Silly Thanks to Prime Day

Amazon Moves Fast, Roborock Qrevo S5V Is 40% Off Barely a Week After Hitting the Market

The Phantom of the Opera Has a Lot of Demands for His Immersive Masquerade

Prime Day Shopping: How to Get the Deals Without Getting Scammed

Grab Prime Day Laptop Savings: My Go-to Acer Aspire 14 AI Is Nearly 30% Off at Costco Right Now

Today's NYT Strands Hints, Answers and Help for July 9 #493

Today's NYT Connections Hints, Answers and Help for July 9, #759

Today's NYT Connections: Sports Edition Hints and Answers for July 9, #289

Best Vacuum for Hardwood Floors in 2025

Best Cheap Vacuums for 2025: Our Best Lab-Tested Performers for Less Than $300

It's Nearly Time for Samsung's Galaxy Z Fold 7 and Z Flip 7 Debut: How to Watch the Unpacked Event

8 Best Amazon Prime Day Vacuum Deals for Dust and Dirt in 2025

From Point Clouds to Photorealism: How PRoGS Advances the State of Neural Rendering

Elon Musk lashes out at Tesla bull Dan Ives over board proposals: 'Shut up'

Apple says COO Jeff Williams will retire from company later this year

A Fast-Rising Gaming YouTuber Is an AI Construct, Not a Human

OpenAI May Be in Major Trouble Financially

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

Prime Day pick: Save a record 33% on the Sonos Ace headphones

Aqara HomeKit smart locks, cameras, and more offer Prime Day discounts of up to 38%

Apple COO Jeff Williams stepping down later this month

You can (finally) buy the Nintendo Switch 2 on Amazon now (but don't expect a Prime Day deal)

M&S confirms social engineering led to massive ransomware attack

Samsung announces major security enhancements coming to One UI 8

The 25 best Prime Day 2025 deals under $25

5 surprise products Samsung may unveil at Unpacked tomorrow - including a tri-foldable phone

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