ChatGPT for Math Review

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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 $A + B$

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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ai4science03 2024-09-09 12:38
5.0
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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ai4science03 2024-09-09 12:33
5.0
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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ai4science03 2024-09-09 12:20
4.0
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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