The U2723QE covers the entire sRGB color space and has excellent coverage of AdobeRGB and DCI-P3.ĭell’s monitor also excels on the connectivity front. The monitor’s 27-inch 4K display offers crisp images and text. This impressive monitor packs an IPS Black panel, providing a better contrast ratio than regular IPS-type displays while keeping the traditional IPS advantages, such as wide viewing angles and exceptional color accuracy. A 2022 addition to this lineup-the Dell U2723QE-is no exception. After all, they offer excellent picture quality and color accuracy. RELATED: How to Pick the Right Monitor for Your PC Best Mac Monitor Overall: Dell U2723QE Dellĭell’s USB-C-equipped Ultrasharp series monitors are popular. With the basics out of the way, now it’s time to jump into our recommendations. So you can choose the resolution that fits your budget.įor more helpful information about buying a monitor, you can check out our detailed explainer on how to pick the right monitor. Although 4K has become quite common, QHD resolution provides an excellent middle ground between 4K and Full-HD resolutions. Screen resolution is another important part of a monitor. For example, creative professionals prefer color accuracy and better coverage of different color spaces, whereas gamers will want a high refresh rate panel and low input lag. Aside from asking the monitor manufacturer to confirm the support, you can check reviews and customer feedback on retail sites.īesides compatibility and input support, your budget, available space, intended usage, and display size are also crucial. While buying a monitor, you also have to check if it’s compatible with Macs, particularly if you are using the new Apple Silicon-powered machines. In an ideal world, you should be able to pick any monitor and expect it to work flawlessly with your Mac. For MacBooks that only include a Thunderbolt port, monitors with Thunderbolt or USB-C support are your only option. Depending on which Mac you are using, you can connect to a monitor one of two ways- Thunderbolt via USB-C or an HDMI port.Īs the Thunderbolt port is more versatile than the HDMI port, picking up a monitor with USB-C/Thunderbolt input is better for reducing cable clutter. Most importantly, you want a monitor that works seamlessly with your machine. While the monitor market offers many options, you must keep a few things in mind before picking one up for your Mac. What to Look for in a Mac Monitor in 2023 What to Look for in a Mac Monitor in 2023 Best Mac Monitor Overall: Dell U2723QE Best Budget Mac Monitor: Gigabyte M27Q Best Premium Mac Monitor for Professionals: Apple Pro Display XDR Best Mac Monitor for Creatives: BenQ SW271C Best Ultrawide Mac Monitor: BenQ PD3420Q Best Gaming Mac Monitor: Acer Predator XB273U Update, : We’ve reviewed our recommendations and are confident these are still the best Mac monitors you can buy. ✗ USB-C port can only deliver 10W of power ✓ Wide 34-inch screen with 1440p resolution ✓ Native 4K resolution with excellent color accuracy ✓ Complete coverage of sRGB and near-perfect coverage of DCI-P3 With a 240Hz refresh rate, exceptionally low input lag, and Adaptive-Sync support, this Acer monitor is perfect for gaming. It has a 34-inch screen, super color accuracy, and Thunderbolt 3 support. The BenQ PD3420Q is an excellent ultrawide monitor. In addition, it can display 10-bit color, which is not common in monitors. The BenQ SW271C has a lot going for it, from 4K resolution to outstanding color accuracy. With a stunning design and pro-grade color accuracy, the Apple Pro Display XDR is an excellent monitor for creative professionals, if you can afford the high price. It has a 170Hz screen, superb color accuracy, and excellent coverage of various color profiles. This may be a budget monitor, but Gigabyte doesn't skimp on the features. It also provides a built-in USB hub and KVM switch functionality. The Dell U2723QE delivers excellent picture quality, loads of connection options, and incredible ergonomics.
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* usage of this music organizer app on multiple phones and tablets * $14.99 per year, when paying yearly (~ $1.25 per month) In the app, tap the menu icon top left, then choose Contact Support.ĬLZ Music is a subscription app, costing: We love to hear your feedback, we are here to help with any problems or concerns, 7 days a week. ** Questions or concerns? Just contact us! * Group your albums into folders by author, composer, format, label, genre, location, etc. Sort by artist, title, release date, length, date added etc. ** Browse, sort, group and search your music inventory in many waysīrowse your collection as a list or as a "cover wall" with resizable cover thumbnails! Totals for albums, artists, discs, purchase price, etc., most recent additions, charts by format, artist, release year and genre. ** View collection totals and charts in the Statistics screen Sync data to/from our Music Connect web-based software (separate subscription). Always have an online cloud-backup of your music organizer database.ĥ. View and share your music collection online, using the CLZ Cloud viewer website.Ĥ. Sync your music library between devices (e.g. Share your app subscription to other mobile devices, without paying again.Ģ. Like purchase date / price / store, location, rating, notes, etc.Įdit album entries one by one or use Edit Multiple for batch editing many albums in one go!ġ. * Edit your album entries to add personal info * Automatically download album details, song lists and cover artĪutomatically download cover images, track lists and full album details, like artist, title, label, release date, running times, genre, etc. * Easily add album to your music inventory, using our CLZ Core online music database Organize the CDs and LPs that you own and keep track of the albums that are still on your wish list. * Keep track of your collection and your wish list Easily catalog your collection of CDs and vinyl records. Or you can manually upload your logo to My Brand Kit:Īfter all that’s done, simply customize a template and have your logo and brand color palettes applied for your design in just one click: Once your logo’s ready, you can then access My Brand Kit to have your logo automatically extracted from your website (along with your brand colors): More importantly, with a paid account, you can apply your logo and brand color palettes automatically to any of your Venngage designs. But doing so also gives you access to thousands of templates you can use throughout your company’s communications. It’s free to create your logo, but to download it, you must upgrade your account. Once you’ve done customizing your logo, you can change the color or opacity of the template background if you want a transparent background before downloading: Pro tip: Want to know you can edit icons for your logo? Check out our recommended best icon makers. Venngage offers 40,000+ icons and illustrations you can use for your logo. Use the editor to modify the font, colors and size of the text and scroll through hundreds of options for imagery. Create your logo alongside a suite of other brand materials like pitch decks, presentations, infographics and more so you can be sure everything works harmoniously.Ĭhoose from dozens of templates and customize one using your company name. Venngage’s Logo Maker is a standout option because it doesn’t stand alone. (By the way, Nike’s founders paid only $35 for a young graphic designer to create that logo, though she later was rewarded with Nike stock.) 1. If Nike’s shoes weren’t popular, it’s doubtful we’d remember the brand’s iconic swoosh. Whether you use one of the best free logo makers we’ve listed below or another tool, a good logo itself is secondary to a great company. In fact, anybody with good taste can create one. While many branding and identity companies charge into the six figures for logos and corporate identity services, a great logo does not have to break the bank. The short answer: you can hire a graphic designer, or create one your own using logo maker tools. START CREATING FOR FREE Click to jump ahead: Keep your messaging on-point with Venngage’s Logo Maker. Of course, creating a great logo is just the start, and establishing and reinforcing a strong brand identity requires consistent application of fonts, colors and other brand guidelines. When you think about the biggest brands in the world, chances are you picture their logos, whether they became iconic because the business was successful or the logo helped the organization succeed. The idea of encapsulating your entire brand in a single image like a logo feels overwhelming, but the good news is that there are many free or cheap online logo makers that can help establish the identity of your new business. The medial side of the Nike Air Zoom SuperRep 2 in a men’s colorway. The lateral side of the Nike Air Zoom SuperRep 2 in a men’s colorway. The shoes will come with a $120 price tag. 26 and the global launch is slated for Jan. The release in Europe, the Middle East and Africa (EMEA) will follow on Dec. The Nike Air Zoom SuperRep 2 will first drop in China on Dec. Courtesy of NikeĪside from the updates, the Nike Air Zoom SuperRep 2 features much of the technologies used in the previous shoe such as the forefoot Zoom Air cushioning units for added “pop” on jumps, the reinforced rand made to brace against aggressive lateral movements and the flexible “burpee break” design that allows for the wearer’s foot to be positioned correctly. The Nike Air Zoom SuperRep 2 in a men’s colorway. The rubber provides nearly perfect traction on wood and hard flooring surfaces, holding up during planks and burpees.The Nike Air Zoom SuperRep 2 in a women’s colorway. Perfect traction on wood and hard flooring The cushioning works very well in high-impact situations and remains stable on hard lateral moves. While rocking forward and doing jump rope hops, the shoes actually rock my foot forward. At no point did I feel like I was going to roll my ankle. Although they’re bulky with super chunky sole units, they remained stable on side-to-side movements. The good news on these shoes is that on exercises like mountain climbers, burpees, and skater jumps, they play their role quite well. Maybe thicker socks could solve the issue, but throughout the cardio workouts, I had to stop multiple times to adjust the laces. If they were too loose, there was heel slippage. If I tied the laces too tight, they dug into my foot, along with the collar and the edges of the gusseted tongue. Locking my foot down, however, was a little bit of a challenge. They are a little bit narrow in the toe area, but not to the point of discomfort. The SuperRep 2 is relatively true to size by Nike standards. Making sure we know who made the shoe, Nike slapped a giant swoosh on the lateral side, and a smaller swoosh printed on the medial side. The medial side is a lined neoprene material.Īsymmetrical lacing is featured, with the lateral sides holding 4 loops of hidden nylon webbing and the medial with 4 ovular plastic eyelets. The lateral side of the shoe is a ribbed mesh material, that runs from the toe-cap area around to the heel, tapering at the arch of the foot. The upper is also kind of its own creature The forefoot is significantly thicker and more sculpted than the rest of the liner. Directly underfoot is a PU footbed, designed specifically for this model. The FlyPlate I had previously mentioned runs from about mid-heel to the metatarsal heads, which is on the front end of the Zoom Air units. The heel piece is a beveled horseshoe-shaped slab of EVA, with a rubber outsole along the perimeter of the bottom of the shoe. In front of the Zoom units, there is a deep V-groove and a rubber toe-off outsole piece. In true Nike fashion, a translucent rubber outsole allows the wearer to see the cushioning technology from the bottom, as well as the sides. In the forefoot, there are two visible Zoom Air units, placed strategically underneath the ball of the foot, and mirrored on the lateral side. The forefoot and heel of the midsole and outsole are two different pieces, bridged together by what Nike calls a FlyPlate. In all of my years looking at any buying athletic shoes, I’ve seen very few that are as radical as the SuperRep 2.
No Linking or Cross-posting to Other Subreddits This is not about trying to exclude anyone, it is simply that if you are related to Gamestop, the merchandising bots target you. As such, the best solution was simply to require a account age restriction. Our mod team is small and does not have the capabilities of larger subs. We get dozens of spam posts/comments every day of bots linking to merchandize scams, random penny stocks, and more. Words and jokes that are tolerated on other subreddits are not tolerated here (do not make $rope jokes, no “wife's boyfriend” stuff, etc.) It is highly recommended you do not use the word “retard” (even though apes do) as reddit has issued bans for this.Īccounts Must be Older than 1 Month to Contribute Toxicity is a challenging topic to define, but includes (but is not limited to) racism, ableism, sexism, homophobia, transphobia (including things like intentional misgendering or deadnaming), bad takes about nationalities or religions, etc. This Subreddit has a Near-Zero Tolerance for Toxicity – Including Jokes About Suicide and Ableism This rule exists because in the early days of the sub, people were doing nothing but spamming posts about “Please explain why the MOASS can't happen.” Discussion may occur within the thread, but may not be the main purpose of the thread. Mercilessly.įinancial Discussion is Limited to the Lounge. Do not flood the sub when the stock is up 10%. Do not do your typical LARPer "oh have you heard of GME?" "Oh, is that the stock with." shit in this subreddit, you will be banned. If it can be said in the shill agenda or the chat, it doesn't need a new post.Īll rules are suspended in the event of ape brigades, which is for purposes of this sub defined as two or more apes attempting to subvert the narrative of this sub. Also low effort text posts will be removed. Pointless spam promoting stocks will be removed and may result in a ban – this is not an ape sub. Sharing opinions on stocks (even if they dissent from the subreddit's primary focus) is permitted, however prepare for likely ridicule if you post favorable opinions about a meltdown stock. No Ticker/emoji spam, shilling or low effort Only partially blurred user or sub names, PFPs, or sub logos are not allowed and the post will be deleted. This is to discourage people from attempting to locate a post, comment, and/or user to brigade. When posting screenshots of content on Reddit, you must blur usernames, profile pictures, subreddit names, subreddit logos, and user and post flairs (if the flair mentions the subreddit's name). Usernames, Reddit PFPs, Subreddit Names, and Sub Logos Must be Blurred Out When Sharing Screenshots This can affect which services appear on our site and where we rank them. While we strive to keep our reviews as unbiased as possible, we do receive affiliate compensation through some of our links. Our mission is to help consumers make informed purchase decisions. Clarify all fees and contract details before signing a contract or finalizing your purchase. For the most accurate information, please ask your customer service representative. Pricing will vary based on various factors, including, but not limited to, the customer’s location, package chosen, added features and equipment, the purchaser’s credit score, etc. (Or it might not-which is why you should ask!)ĭisclaimer: The information featured in this article is based on our best estimates of pricing, package details, contract stipulations, and service available at the time of writing. If the accounting firm uses QuickBooks but you’ve used Zoho Books to this point, transferring your financial data into a new accounting software package might cost extra. If you’re planning to work with a bookkeeping company rather than hiring a solo bookkeeper, make sure to ask about its accounting system. Some bookkeeping companies and accounting firms use proprietary in-house accounting software. (For example, QuickBooks Online’s cheapest plan allows for just one business user, but it includes accountant access at no additional cost.) Regardless of the accounting system you use, you should be able to share it with a bookkeeper come tax time with no problems. However, you can share most accounting solutions with an accountant or bookkeeper, including accounting software that otherwise limits its users by plan. Oracle NetSuite and FreshBooks are two other popular bookkeeper software options. Most bookkeepers and accountants use the same popular software small-business owners do, especially QuickBooks Online, Xero, and Sage. (Notably, QuickBooks Online offers 50% off for three months or a 30-day free trial, so be prepared to forego one of them if you want to test drive your software.) Finding the best bookkeeping software for you is crucial to your business’s success-try as many options as you need to settle on one you feel confident in. Luckily, most bookkeeping software comes with a free trial. And both Sage Business Cloud Accounting and Kashoo have more solid customer service. FreshBooks has much better invoicing with clear, color-based reports. (For one thing, it starts at an above-average monthly price.) Xero and Wave Accounting are more affordable with similar reporting features. Its comprehensive reports are easy for first-time business owners to generate and understand, and it offers more thorough reporting than just about any other software out there.īut QuickBooks Online isn’t necessarily the best online accounting solution for you. QuickBooks Online is one of the most popular bookkeeping software choices in the US. In the videos of the channel affinity tutorials the problem that there is no cursor on the Apple tablet was also considered - the use of the display is shown via video splitting in addition to the screen tap. If you are looking for special functions or tools, just add them in the YouTube search field ) First Affinity Photo iPad tutorials in GermanĪs I scrolled around on YouTube, in the middle of researching this article, I also found the first videos for the iPad version. If you want to scroll through the search results of the entire offer in general, then here is my list of results. During a first, quick search, I found three channels with a few tutorials for image editing with Affinity Photo for Mac and Windows: Hofnaar, Affinity Jack and virtual photo art. YouTube is of course one of the first places to go if you want tutorials for programs in German. Help and how-to videos on YouTube (German) The designer and graphic artist software will in 94 videos on its own channel helpful and explained in terms of various features and tools. A similar offer is also available for Affinity Designer. 210 videos invite you to discover and learn. This is also possible on the Affinity Photo Vimeo account. Sure, Vimeo is not as popular as YouTube, but you can find videos there with less distraction, without advertising and with a content-focused design. In addition to the photo editing software, the Affinity Designer (another app) themed. There is also a forum with help and support so that your questions can be answered quickly. The site is a good place to go there is exactly what the name suggests: tutorials. Especially if it is “only” special handles and tools that you are looking for, and not a complete introduction with theoretical treatises on digital photography, file structure, formats such as JPEG, RAW, etc. Of course you can also find instructions outside of the printed word to work with the Serif program. Just click on the Share button, then click on the embed code, copy it, and paste in InDesign.Īlso, you can click on Show Options and decide whether to include things like the title, byline, text link, etc, before copying the code.12,45 EUR Buy it at Amazon Price includes VAT, plus shipping costs (updated: at 15: 42 clock) Affinity Photo instructions online: step by step on the Internet To see an example, check out this Publish Online document, featuring the silly but incredibly popular Pen-Pineapple-Apple-Pen song.īy the way, this same trick for Vimeo videos too. But as long as you have an internet connection, the video will play inside the EPUB. Note that the EPUB will not pass a validation check because the YouTube video is a remote resource not listed in the content.opf file inside the EPUB package. Then export to EPUB 3 and/or Publish Online. You can preview the video in the EPUB Interactivity Preview Panel. Position the video frame where you want it in your layout. That won’t show up in your exported file. Don’t worry if it shows an error message. Then you’ll see a full-size frame where the video will be. At first, you’ll see a small square while InDesign is checking the embed code. Make sure nothing is selected, and then paste. Then in the controls under the video, click Share, and then Embed.Ĭopy the full embed code. Ever wish you could include YouTube content in an interactive document exported from InDesign? You can do it if you export to EPUB 3 (fixed-layout or reflowable) or Publish Online.įirst, go to YouTube and find the video you want. We cannot guarantee product will not contain traces of these allergens. Produced in a kitchen where NUTS, SESAME and OTHER ALLERGENIC INGREDIENTS are used. Our chocolate filling cream also contains 20% Chocolate (100% Cocoa Solids).ĪLLERGENS Our Cakes are not suitable for people with food allergies. Suitable for Vegetarians.īutter ( milk), Sugar, Vanilla Flavour, Milk. Sugar, Wheat Flour, Egg, Water, Vegetable Oil (Rape), Skimmed Milk Powder, Glycerine, Cocoa Powder, Dextrose, Maize Starch, Raising Agents E450, E500, Salt, Vanilla Flavour, Colours: E124, E129, Preservative E202, Xanthan Gum.Ĭontains Gluten, Egg. Sugar, Wheat Flour, Egg, Water, Vegetable Oil (Rape), Fat Reduced Cocoa Powder, Glucose, Skimmed Milk Powder, Glycerine, Dextrose, Maize Starch, Raising Agents: E500, E450, Salt, Natural Vanilla Flavouring, Potassium Sorbate, Xanthan Gum. Sugar, Wheat Flour, Egg, Vegetable Oil, (Rape), Skimmed Milk Powder, Glycerine, Dextrose, Maize Starch ,Raising Agents (E450, E500), Salt, Vanilla Flavouring, Preservative (E202), Xanthan Gum. Sugar, Wheat Flour, Egg, Vegetable Oil (Rape), Water, Glycerine, Modified Maize Starch, Raising Agents (E450, E500), Cocoa (3%), Salt, Vanilla flavour, Colours: E124 & E129, Preservative E202, Emulsifiers: Xanthan Gum, Soy Lecithin Vanilla Cupcake Sponge Ingredients For a quarter sheet cake, you pay 31.49 while a half sheet cake costs 47.99. Sugar, Wheat flour, Egg, Vegetable Oil (Palm and Rape, Emulsifier E471), Skimmed Milk, Belgian Chocolate (5%), Glycerine, Dextrose, Raising Agent (E450, E500), Cocoa, Salt, Preservative E202, Stabilizer (E415), Colour E155, E133, Soy Lecithin Red Velvet Sponge Ingredients Giant Eagle’s Paw Patrol cake is available in three different sizes. Sugar, Wheat flour (contains Gluten ), Egg, Vegetable Oil, Water, Skimmed Milk Powder, Glycerine,Raising Agent (E450a, Sodium Bicarbonate), Salt, Emulsifier E415, Preservative E202, Vanilla Flavour, Soy Lecithin. "4EVA," the Pharrell-assisted lead single, has a sticky, propellant chorus resting pleasantly in the pocket between sweaty nightclub dance floor and tipsy summer block party. On the opener he claims to be "one of the few men who know where the clit is." His hooks are sterling - gruff and plosive when the occasion calls for it, lithe and limber elsewhere. Aminé raps with more cheeky temerity here than he has perhaps anywhere else. From the very first track, "Who He Iz," to the triumphant two-part closer, "K&A," the record runs like a compilation of their best musical instincts compressed, refined and fine-tuned to a punchy summer frequency. And, if any wrinkles were left, they've been smoothed out on KAYTRAMINÉ. It feels somewhat like kismet that, despite their different arcs and very different approaches, Kaytranada and Aminé's trajectories have led them right back to one another. For Aminé, this has culminated in projects like 2020's Limbo - a collection of the buoyant, melodic raps he made his name on, some trunk-rattling trap and a marked progression in vocal technique-and 2021's TWOPOINTFIVE, a 26-minute, frenetic sugar rush of dexterous rhyming and dazzling hooks. His major label debut, Good For You, was suffused with the same kind of technicolor juvenility that propelled his breakout single, but as the years have progressed, the now-29-year-old has diversified his sound and settled into a more relaxed pose. After Calling Brio, the Portland rapper was very suddenly catapulted into the mainstream as a precocious, gap-toothed provocateur with 2016's "Caroline." The single - a massive streaming hit that has been registered 6x platinum - bears all the hallmarks of what would become Aminé staples: a goofy affability, staccato bursts of irreverent wordplay and a sticky pop hook. These days, the introvert-cum-superstar commands top-billing at Coachella (performing before a giant replica of his own head), and owns two Grammys.Īminé, for his part, has also undergone a bit of a transformation. His full-length debut, 99.9%, released on XL, was awarded Canada's prestigious Polaris Music Prize. All the while, his lore only grew, attracting the admiration and attention of more famous peers. Despite touring the globe, playing festivals and opening for acts like Madonna, the chronically shy 23-year-old continued to live in the basement of his mom's home in suburban Montreal, sharing a bedroom with his younger brother. His favored reverb-y hand claps, crisp hi-hats and extraterrestrial synths had become a bit of a calling card. In 2014, the Haitian-Quebecois producer had made a name for himself as a kind of remix savant, molding R&B classics like Janet Jackson's "If" and TLC's "Creep" into swinging club tracks and thumping beat-scene anthems. Since that fateful early exchange, the artists' respective sounds have evolved with their profiles. The ace 11-track album, replete with a radio-worthy single and a some of the best crafted verses and beats of their respective careers, is emblematic of artists who, not only have migrated from the margins to the mainstream, but are operating with a level of comfort and confidence that they could have previously only dreamed of. If this origin story - a shot in the dark becoming a pivotal career turning point - is the prologue, then KAYTRAMINÉ, their new collaborative project, is a fitting afterword. It was a moment that established Aminé's swaggering hip-hop-outsider persona and provided proof of concept for his ebullient brand of pop-rap. The free beats that Kaytranada sent back eventually ended up on his mixtape, Calling Brio, a project that ingratiated the Portland rapper with the music blogosphere and, ultimately, helped earn him a spot alongside megawatt acts like Ariana Grande and The Weeknd at Republic Records. "I was broke as f*** working on music everyday in 2014 looking for a north star," he recalled on Twitter last week. His signature bounce, Aminé hoped, would provide the boost he was looking for. Said producer, Kaytranada, already had a growing cult following on SoundCloud and an iconic Boiler Room set. The then-20-year-old soon-to-be dropout at Portland State University hoped a few beats from a buzzing DJ and producer in Montreal would help give him some much needed juice. In July of 2014, the marketing student and would-be rapper Aminé sent out a wishful Twitter DM attempting to get his fledgling music career off the ground. In short, counted twice were the elements of A∩ B. Which are they? The elements that were counted twice are exactly those that belong to A (one count) and also belong to B (the second count). Indeed, in | A| + | B| some elements have been counted twice (the common siblings of the two brothers). If A and B are not disjoint, we get the simplest form of the Inclusion-Exclusion Principle: (2) (Consider also such a question: two brothers have three siblings each. and this is how - by following its plot - we arrived at where we are today: masters of a vast amount of accumulated knowledge in control of fantastically powerful technology that could not have been foreseen at the beginning of the story. Well, what can one say? Is it not what is called Turning an idea around in one's mind? Once the humankind began composing the story of counting, the plot acquired life and logic of its own. Is it not too artificial to count sets that are not disjoint? After all, this would never happen with counting by grouping. The latter form is suggestive of the question, What if A and B are not disjoint? Or is it? with no common elements) wholes and combine them into one. Instead of splitting the whole into two groups, we start with two ( disjoint, i.e. This is exactly same statement with a somewhat different emphasis. Since X = A∪ B, the idea of counting by grouping can also be expressed as (1) We shall consider that statement on its own merits. If a group of objects X is split into two groups - denoted A and B, which means that they have no common elements ( A∩ B = Ø) and together combine into the whole ( X = A∪ B), then the number of elements | X| in the group X can be arrived at by first counting elements of A and then counting elements of B. The latter is a statement of legitimacy of counting by grouping. If X = A ∪ B and A ∩ B = Ø, then | X| = | A| + | B|. Every group of objects A can be associated with a quantity - denoted | A| - called the number of elements in A.The second describes its fundamental property. The first just states that counting makes sense. The Principle itself can also be expressed in a concise form. From the First Principle of Counting we have arrived at the commutativity of addition, which was expressed in convenient mathematical notations as a + b = b + a. |