Example. $V_1$ and $V_2$ are subspace of $\mathbb{R}^2$ over $\mathbb{R}$. Any vector (red vector) can be uniquely determine by scalars of vectors in $V_1$ and $V_2$. The intersecion of $V_1$ and $V_2$ is the trivial subspace $\{\vec{0}\}.$
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The language I mentioned in the last class is an axiomatic system. An axiomatic system is a set of axioms used to logically derive theorems. For example, in Euclidean geometry, the statement “a line can be drawn between any two points” is considered an axiom—a fundamental truth accepted without proof....
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AI poses a potential challenge to human intelligence. We train AI models by having computers mimic human behavior, much like a baby learning, and this training successfully demonstrates aspects of human intelligence. However, we as humans still hesitate to acknowledge that AI’s intelligence is comparable to human intelligence. Among the...
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