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What is Class Counter in Maths



In 2009 Dusa Macduff goes to a talk at the Numerical Sciences Exploration Foundation in Berkeley, California. The speaker was Katrin Wehrheim, who was then an associate teacher at the Massachusetts Establishment of Innovation. In his discourse, Wehrheim provoked the symplectic math local area to face blunders in basic strategies grew over 10 years sooner.  reviewed Macduff, who was one of Wehrheim’s doctoral proposal analysts.

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Barnard School mathematician Dusa Macduff battled for a really long time to address what she saw as holes in the underpinnings of symplectic calculation.

The test was private for Macduff. In 1999 he composed an overview article that depended on hazardous major methods by one more sets of mathematicians, Posse Liu and Pack Tian. Presently, after 10 years, Wehrheim was bringing up that Macduff’s paper – in the same way as other early papers in symplectic math – including Fukaya’s – had mistakes, specifically how to move from nearby to worldwide in the worldwide calculation of focuses. Subsequent to paying attention to Wehrheim, Macduff concluded that she would attempt to address any slip-ups.

“I had a terrible heart about what I composed in light of the fact that I knew some way or another it was not completely exact,” she said. “I commit errors, I comprehend individuals commit errors, yet on the off chance that I commit an error, I attempt to address it, and in the event that I can’t, it’s off-base.”

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Macduff and Wehrheim started work on a progression of papers that were brought up and fixed as missteps in Fukaya’s treatment of transversality. In 2012 Macduff and Wehrheim moved toward Fukaya with their interests. Following 16 years in which his work was ignored by the numerical local area, he was happy he was intrigued.

“In 2012 we got K. There was an unmistakable protest from Wehrheim. We were extremely glad to have this since it was the primary significant numerical reaction we got on our work.

To examine the protests, mathematicians framed a Google Gathering in mid 2012 that included Macduff, Wehrheim, Fukaya and Ono along with two of Fukaya’s later partners, Yong-gyun Gracious and Hiroshi Ohta. The conversation by and large follows this structure: Wehrheim and Macduff will bring up issues about Fukaya’s work. Fukaya and his associates would then compose long, itemized replies.

Whether those answers were agreeable relied upon who was understanding them. According to Fukaya’s perspective, his work on Qur’anic structures was finished and right all along. I don’t think there was anything missing,” he said.

Others clash. After the Google Gathering conversation finished, Fukaya and his associates posted a few papers on Quranic structures that together ran for in excess of 400 pages. Hofer feels that the length of Fukaya’s reactions is proof that Macduff and Wehrheim’s incitement was essential.

“By and large, [Fukaya’s approach] worked, however it required more clarification than was initially given,” he said. “I think Fukaya and Ono’s unique paper was a little north of 100 pages, and because of this conversation on the Google bunch they delivered a 270-page composition and a couple hundred pages making sense of the first outcomes. So certain. Obviously required explanation.”

Abujaid concurs that there was a slip-up in Fukaya’s unique work.Simultaneously, he feels that Qur’anic develops are by and large the correct method for managing transversality issues. He views the blunders in the 1996 paper as happening on the grounds that the symplectic math local area was not adequately evolved at an opportunity to audit the new work appropriately.

“The paper ought to have been refereed all the more cautiously. My perspective is that with a decent ref report of a few adjusts that the paper would have been faultless and everything looks great,” said Abujaid.

In August 2012, after a Google Gathering conversation, McDuff and Wehrheim posted an article they had started composition before the conversation definite ways of revising Fukaya’s methodology. He later refined and distributed that paper with two others, and plans to compose a fourth paper regarding the matter. In September 2012, Fukaya and his co-creators posted a portion of their reactions to the issues raised by Macduff and Wehrheim. To Fukaya, Macduff and Wehrheim’s papers didn’t propel this region essentially.

“It is my viewpoint that the papers he composed don’t contain new and significant thoughts. There is absolutely a few contrast from the previous papers of our own and others. Notwithstanding, the thing that matters is just on a little detail,” FukAya said in an email.

Hofer imagines that this understanding short sells the commitments of Macduff and Wehrheim. From his perspective, the pair accomplished something other than fix little specialized subtleties in Fukaya’s work – they tackled significant level issues with Fukaya’s methodology.

“They comprehended the various pieces well overall and how they cooperated, so you couldn’t simply say: ‘Here, assuming it’s risky, I fixed it locally,'” he said. “You should know where pretty much another issue would emerge. He grasped it at an exceptionally undeniable level.”

How mathematicians assess the significance of mistakes in Fukaya’s 1996 paper and the commitments Wehrheim and Macduff made to address them mirrors a polarity in the manner we ponder the act of science.

“Arithmetic has two ideas,” Abuzaid said. “Arithmetic is this way: the money of math is thought. Also, science is the cash of arithmetic is verification. It is hard for me to say which side individuals stand on. My own perspective is: overwhelmingly significant in science is thought, And there’s proof to ensure that contemplations don’t wander off.”

Fukaya is a geometer with a sense to think in overgeneralized terms. Conversely, Wehrheim is prepared in examination, a field known for its thorough regard for specialized subtleties. In a profile for the MIT site Ladies in Math, she expressed that in math, “we don’t compose great papers any longer,” and looked at mathematicians who don’t tell the subtleties of their work to climbers who arrive at the top. Mountains without leaving snares on the way. “Somebody with little preparation would have not a chance of following it without tracking down a way for themselves,” she said.

These contrasting assumptions for what considers an adequate measure of detail in a proof caused a lot of pressure in the symplectic calculation local area around the protests of Macduff and Wehrheim. Abuzaid contends that it is essential to be shrewd while bringing up botches in crafted by another mathematician, and Wehrheim might not have been strategic enough in this. “Assuming that you present it as: ‘All that has preceded us is off-base and presently we will offer the right response,’ that is probably going to set off some kind of issue of need claims,” he said. .

Wehrheim declined different solicitations to be evaluated for this article, saying she “needs to stay away from additional politicization of the subject.” In any case, Macduff feels that he and Wehrheim had no real option except to be enabled to bring up the defects in Fukaya’s work: it was the best way to definitely stand out.

“It resembles being an informant,” she said. out with you. what’s more, not from individuals who can be off-base.”

Notwithstanding who gets the credit for fixing the issues with Fukaya’s paper, they have been fixed. In the beyond couple of years, on account of arithmetic, the debate encompassing his work has been settled.

These issues were felt and ultimately fixed,” Eliashberg said. “Perhaps it superfluously makes a ton of energy in certain gatherings, however generally speaking I think everything was dealt with and things will go on.”


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Kickass Proxy: Accessing Torrents Safely and Anonymously




In today’s digital age, accessing content online has become easier than ever. However, some content, such as torrent files, may be restricted or inaccessible due to geographical limitations or legal issues. This is where Kickass Proxy comes into play, offering a solution to bypass these restrictions and access torrents safely and anonymously.

Introduction to Kickass Proxy

Kickass Proxy, also known as KAT Proxy, is a mirror website that replicates the content and functionality of the original Kickass Torrents website. It allows users to access torrents and download files without directly connecting to the original website, which may be blocked or inaccessible in certain regions.

What is a Proxy Server?

Before delving deeper into Kickass Proxy, let’s understand what a proxy server is. A proxy server acts as an intermediary between your device and the internet. When you connect to a website through a proxy server, your device’s IP address is hidden, and the proxy server’s IP address is used instead. This enables users to bypass censorship, access blocked content, and maintain anonymity online.

Why Use Kickass Proxy?

Accessing Restricted Content

One of the primary reasons users turn to Kickass Proxy is to access content that may be restricted or blocked in their region. By connecting through a proxy server, users can bypass these restrictions and access torrents, movies, music, and other files that may not be available through conventional means.

Privacy and Anonymity

Privacy concerns are prevalent in today’s digital landscape, with ISPs and government agencies monitoring online activities. Kickass Proxy offers users a way to maintain their anonymity while accessing torrents, ensuring their online activities remain private and secure.

Bypassing Geo-Restrictions

Certain websites and content platforms impose geo-restrictions, limiting access to users based on their location. Kickass Proxy allows users to bypass these restrictions, enabling access to torrents and other content regardless of geographical location.

How to Use Kickass Proxy Safely

While Kickass Proxy offers numerous benefits, it’s essential to use it safely and responsibly to avoid potential risks and legal consequences.

Use a Reliable Proxy

When using Kickass Proxy, opt for reliable and trusted proxy servers to ensure a secure connection and avoid potential security risks.

Ensure HTTPS Connection

Always ensure that the proxy server you’re using supports HTTPS connections to encrypt your data and protect it from prying eyes.

Enable Firewall and Antivirus Protection

To mitigate the risk of malware and security threats, enable firewall and antivirus protection on your device before accessing Kickass Proxy or any other torrent website.

Popular Kickass Proxy Alternatives

In addition to Kickass Proxy, several other proxy websites offer similar functionality, including The Pirate Bay Proxy, RARBG Proxy, and 1337x Proxy. These alternatives provide users with additional options for accessing torrents and downloading files securely.

Legal Issues and Risks Associated with Using Kickass Proxy

While Kickass Proxy provides users with a convenient way to access torrents, it’s essential to be aware of the potential legal issues and risks involved.

Copyright Infringement

Downloading copyrighted material without authorization is illegal and may result in legal consequences, including fines and penalties.

Malware and Security Risks

Torrent websites, including Kickass Proxy, are often targeted by cybercriminals who distribute malware and malicious software. Users should exercise caution and ensure they have adequate security measures in place when accessing torrents.

Legal Consequences

Using Kickass Proxy to access copyrighted material or engage in illegal activities may lead to legal action by copyright holders or law enforcement agencies. Users should be aware of the legal risks and consequences associated with torrenting.

The Future of Kickass Proxy and Torrenting

As technology continues to evolve, the landscape of torrenting and online piracy may undergo significant changes. While Kickass Proxy and similar websites provide a temporary solution to accessing torrents, advancements in anti-piracy measures and legal enforcement may pose challenges to their continued operation.


Kickass Proxy offers users a convenient way to access torrents safely and anonymously. However, it’s essential to use it responsibly and be aware of the legal and security risks involved. By following best practices for safe torrenting and staying informed about the evolving landscape of online piracy, users can enjoy the benefits of Kickass Proxy while minimizing potential drawbacks.


  1. Is it legal to use Kickass Proxy?
    • While using Kickass Proxy itself is not illegal, downloading copyrighted material without authorization is against the law in many countries.
  2. Are there any alternatives to Kickass Proxy?
    • Yes, several alternative proxy websites, such as The Pirate Bay Proxy and RARBG Proxy, offer similar functionality.
  3. How can I ensure my safety when using Kickass Proxy?
    • To stay safe when using Kickass Proxy, use reliable proxy servers, ensure HTTPS connections, and have firewall and antivirus protection enabled.
  4. What are the risks of using Kickass Proxy?
    • Risks associated with Kickass Proxy include potential malware infections, legal consequences for copyright infringement, and privacy concerns.
  5. Is Kickass Proxy the only way to access torrents anonymously?
    • No, there are several other methods, such as using a VPN or Tor, to access torrents anonymously without relying on proxy servers.

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Blooket Login: Revolutionizing Learning with Gamified Education




In today’s digital age, education is continuously evolving, driven by technological advancements and innovative approaches. One such innovation that has gained significant traction in recent years is gamified learning platforms. Among these platforms, Blooket stands out as a dynamic and engaging tool that transforms traditional education into a captivating gaming experience. With its intuitive interface, customizable content, and collaborative features, Blooket has revolutionized the way students learn and teachers teach.

Understanding Blooket

Blooket is an online platform designed to gamify the learning experience, making education more interactive and enjoyable for students of all ages. Launched in 2020, Blooket has quickly gained popularity among educators worldwide for its ability to engage students and enhance learning outcomes.

At its core, Blooket offers a wide range of customizable games, or “Blooks,” covering various subjects such as math, science, history, and language arts. Each Blook is designed to reinforce specific learning objectives while keeping students motivated and entertained. From multiple-choice quizzes to flashcard challenges, Blooket offers diverse game modes to suit different learning styles and preferences.

The Blooket Login Experience

Accessing Blooket is simple and straightforward, thanks to its user-friendly login process. Students and teachers can create accounts using their email addresses or sign in through Google or Clever accounts. This seamless login experience ensures quick and hassle-free access to Blooket’s extensive library of educational games.

Upon logging in, users are greeted with a visually appealing dashboard that provides easy navigation to different features and functionalities. Teachers have access to administrative tools that allow them to create, customize, and assign Blooks to their students. Meanwhile, students can explore a variety of Blooks recommended by their teachers or search for specific topics of interest.

Features and Benefits

1. Customizable Content:

One of the key features that sets Blooket apart is its flexibility in content creation. Teachers can tailor Blooks to align with their curriculum and learning objectives, ensuring relevance and effectiveness. Whether it’s adapting existing games or creating new ones from scratch, Blooket empowers educators to personalize the learning experience according to the needs of their students.

2. Engaging Game Modes:

Blooket offers a diverse array of game modes, each designed to captivate and challenge students in unique ways. From “Tower Defense” to “Battle Royale,” these game modes leverage gamification principles to promote active participation and critical thinking. By presenting educational content in a gaming context, Blooket makes learning more enjoyable and memorable for students.

3. Collaborative Learning:

Another notable feature of Blooket is its emphasis on collaboration and teamwork. Students can join live games with their classmates, competing against each other or working together to achieve common goals. This collaborative approach fosters a sense of camaraderie and encourages peer-to-peer learning, enhancing overall engagement and comprehension.

4. Performance Tracking:

Blooket provides real-time feedback and performance tracking capabilities, allowing teachers to monitor student progress and identify areas for improvement. Through detailed analytics and reporting tools, educators can assess individual and class-wide performance, enabling data-driven decision-making and targeted intervention strategies.

Real-World Applications

The impact of Blooket extends beyond the classroom, with applications in various educational settings and contexts. Whether used for remote learning, hybrid classrooms, or in-person instruction, Blooket offers a versatile platform that adapts to diverse teaching environments. Its accessibility and ease of use make it an ideal tool for educators seeking innovative ways to engage students and enhance learning outcomes.


In conclusion, Blooket represents a paradigm shift in education, harnessing the power of gamification to make learning more interactive, immersive, and enjoyable. By integrating game-based elements into the curriculum, Blooket promotes active engagement, collaboration, and mastery of key concepts. With its intuitive interface, customizable content, and robust features, Blooket has emerged as a valuable asset for educators looking to transform traditional teaching methods and unlock the full potential of their students. As technology continues to shape the future of education, platforms like Blooket are leading the way towards a more dynamic and inclusive learning experience for all.

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Tech A Comprehensive Guide




Introduction to has rapidly emerged as a powerful platform in the online world, offering individuals and businesses alike an opportunity to showcase their creativity, expertise, and products to a global audience. In this article, we delve into the significance of, its functionalities, and how one can leverage it effectively to enhance their online presence.

What is is a dynamic online platform that allows users to create and share a wide array of content, including articles, images, videos, and more. It serves as a hub for information, entertainment, and inspiration, attracting millions of users from around the globe.

The Importance of in the Online World

In today’s digital age, having a strong online presence is essential for individuals and businesses alike. provides a unique opportunity to reach a vast audience and establish oneself as a thought leader or influencer in a particular niche. Whether you’re a blogger, entrepreneur, or content creator, having a presence on can significantly boost your visibility and credibility.

How to Utilize for Maximum Benefit

Creating Engaging Content

One of the keys to success on is creating content that resonates with your target audience. Whether it’s informative articles, captivating images, or entertaining videos, focus on producing high-quality content that adds value to the platform.

Leveraging SEO Techniques

Optimizing your content for search engines is crucial for increasing visibility on Use relevant keywords, meta tags, and descriptions to improve your chances of being discovered by users searching for similar topics.

Building a Strong Online Presence

Consistency is key when it comes to building a presence on Regularly update your profile with fresh content, engage with other users, and participate in trending discussions to stay relevant and attract followers.

The Role of in Digital Marketing Strategies plays a significant role in modern digital marketing strategies, offering businesses a platform to promote their products and services, engage with customers, and drive traffic to their websites. By incorporating into their marketing efforts, businesses can expand their reach and connect with potential customers in a meaningful way.

Tips and Tricks for Success on

Understanding the Algorithm

Like any social media platform, utilizes algorithms to determine which content to display to users. Understanding how these algorithms work can help you tailor your content strategy to maximize visibility and engagement.

Engaging with the Community

Building relationships with other users is essential for success on Take the time to interact with followers, respond to comments, and participate in discussions to foster a sense of community around your profile.

Utilizing Analytics

Analyzing data and metrics is crucial for optimizing your performance on Pay attention to insights such as reach, engagement, and audience demographics to identify trends and opportunities for improvement.

Case Studies: Successful Utilization of

Explore real-life examples of individuals and businesses who have effectively leveraged to achieve their goals and objectives. From influencers who have built massive followings to brands that have seen significant increases in sales, these case studies offer valuable insights into what works on the platform.

Common Mistakes to Avoid on

While offers immense potential, there are also pitfalls to avoid. From overposting to neglecting engagement, learn from the mistakes of others to ensure your success on the platform.

Future Trends and Developments for

As technology continues to evolve, so too will Stay ahead of the curve by keeping an eye on emerging trends and developments in the platform, and be prepared to adapt your strategy accordingly.


In conclusion, is a valuable platform for individuals and businesses looking to enhance their online presence and reach a wider audience. By creating engaging content, leveraging SEO techniques, and actively engaging with the community, users can maximize their success on the platform and achieve their goals.


1. Is free to use? Yes, is free to use for both individuals and businesses.

2. Can I promote my products or services on Yes, allows users to promote their products and services through various content formats.

3. How can I increase my visibility on To increase visibility on, focus on creating high-quality content, engaging with the community, and optimizing your profile for search engines.

4. Are there any restrictions on the type of content I can share on While allows a wide range of content, it does have guidelines in place to ensure a positive user experience. Be sure to familiarize yourself with these guidelines before posting.

5. Can I track the performance of my content on Yes, provides analytics tools that allow users to track the performance of their content, including reach, engagement, and audience demographics.

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