ChatGPT is one of the leading AI assistants developed by OpenAI Company.
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Let $X$ be a topological vector space. All sets mentioned below are understood to be the subsets of $X$. Prove the following statement: If $A$ and $B$ are compact, so is $A + B$
ChatGPT GPT4o generation produced interesting pictures. This cartoon style images are amazing
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Prompt: Let $X$ be a topological vector space. All sets mentioned below are understood to be the subsets of $X$. Prove the following statement: If $A$ and $B$ are compact, so is $A + B$Truthfully, I am a little bit surprised by the math proof ability and reasoning ability of ChatGPT. To solve the topological math problem, ChatGPT firstly gives a outline of the proof and provides more details to support the proof. The detailed response is as follows: To prove that the sum of two compact sets in a topological vector space X, X is compact, we need to show that if A and B are compact subsets of X, then A+B is also compact. Proof: 1. Recall Definitions and Properties 2. Consider the Projection Maps 3. Use the Compactness of A and B 4. Image of a Compact Set Under a Continuous Map 5. Conclusion: Thus, we have shown that if A and B are compact subsets of a topological vector space X, then A+B is also compact.
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Prompt: ChatGPT GPT4o generation produced interesting pictures. This cartoon style images are amazingChatGPT GPT4o generation produced interesting pictures. This cartoon style images are amazing
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We are witnessing great success in recent development of generative Artificial Intelligence in many fields, such as AI assistant, Chatbot, AI Writer. Among all the AI native products, AI Search Engine such as Perplexity, Gemini and SearchGPT are most attrative to website owners, bloggers and web content publishers. AI Search Engine is a new tool to provide answers directly to users' questions (queries). In this blog, we will give some brief introduction to basic concepts of AI Search Engine, including Large Language Models (LLM), Retrieval-Augmented Generation(RAG), Citations and Sources. Then we will highlight some majors differences between traditional Search Engine Optimization (SEO) and Generative Engine Optimization(GEO). And then we will cover some latest research and strategies to help website owners or content publishers to better optimize their content in Generative AI Search Engines.
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We are seeing more applications of robotaxi and self-driving vehicles worldwide. Many large companies such as Waymo, Tesla and Baidu are accelerating their speed of robotaxi deployment in multiple cities. Some human drivers especially cab drivers worry that they will lose their jobs due to AI. They argue that the lower operating cost and AI can work technically 24 hours a day without any rest like human will have more competing advantage than humans. What do you think?
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Please leave your thoughts on whether human artists will be replaced by AI Image Generator. Some similar posts on other platforms including quora and reddit. Is art even worth making anymore, Will AI art eventually permanently replace human artists, Do you think AI will ever replace artists, Do people really think that replacing artists with ai is a good idea
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