ChatGPT is one of the leading AI assistants developed by OpenAI Company.
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ChatGPT OpenAI
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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 $A + B$
Which is Bigger Number, 9.11 or 9.8?
What's the differentiation of function f(x) = e^x + log(x) + sin(x)?
what's the solution x of equation x^2+5x+6=0?
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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: What's the differentiation of function f(x) = e^x + log(x) + sin(x)?ChatGPT gives the correct answer to the differentiation math problem "What's the differentiation of function f(x) = e^x + log(x) + sin(x)?". It uses the step-by-step thinking and applies the derivative rules for each term, and finally get the overall differentiation result of the function. It' quiet helpful.
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Prompt: what's the solution x of equation x^2+5x+6=0?ChatGPT gives the correct answer to the math problem- a quadratic equation x^2+5x+6=0 and gives the exact answer of x=-2 pr x=-3. It quotes the method of factoring (x+2) (x+3) =0 and gives the detailed steps to solve the question. Even though the method is different from other AI replies using the exact solution of quadratic equation, it's simple and helpful!
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Prompt: Which is Bigger Number, 9.11 or 9.8?I asked ChatGPT the math question which is bigger number and generate the answers using both GPT-4o and GPT-4o Mini. The results are almost exactly the same. And the speed of GPT-4o is almost the same as GPT-4o Mini without feeling much faster? Maybe the answer is too short?
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I asked Gemini to act as an expert in mortgage help me make some calculation of the money that I might lose. The prompts is detailed as I provide as much information as possible, including the original value of the house, how much I already paid, what's the mortgage length and what's the interest rate. But the results are a little bit confusion and the math calculation of the potential money to lose is not very trustworthy. So more improvements are needed. Prompts: 1. You are an expert in mortgage, and I will consult you a few questions about the mortgage of my house. The questions include "I bought my current house in California for about 1 million dollars 4 years ago and paid 10% fees. The mortgage will last 30 years with fixed rate 3%. I've paid the mortgage timely to the bank for 4 years already and I just lost my job. How much money will I lose if I stop paying the mortgage to the bank? 2. Follow up question: "Can you help me make some calculation on how much money will I lose. Do you need some more information?". 3. Third question: "Original loan amount: 0.9 million dollars, Current loan balance: 0.8 million dollars, Estimated property value: 1.1 million dollars"
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I asked ChatGPT to act as an expert in mortgage and help me make some calculation on how much money will I lose if I stop paying the mortgage after 4 years of payment. Overall, I think the interaction is not very helpful. I tried to provide a lot of information in advance, including: Original price of the house is 1 million, I already paid 10%, the mortgage lasts 30 years for 3% interest rate, I've paid 4 years already. " Still, After three rounds of conversation, I still can't get the estimated amount of lost money. So the ability is still a little bit far from satisfactory. The math is a little bit strange and I am not quite sure whether it's correct. Prompts: 1. You are an expert in mortgage, and I will consult you a few questions about the mortgage of my house. The questions include "I bought my current house in California for about 1 million dollars 4 years ago and paid 10% fees. The mortgage will last 30 years with fixed rate 3%. I've paid the mortgage timely to the bank for 4 years already and I just lost my job. How much money will I lose if I stop paying the mortgage to the bank? 2. Follow up question: "Can you help me make some calculation on how much money will I lose. Do you need some more information?". 3. Third question: "Original loan amount: 0.9 million dollars, Current loan balance: 0.8 million dollars, Estimated property value: 1.1 million dollars"
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