Mike_bb's latest activity
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MMike_bb replied to the thread Undergrad Why ##a^0=1##?.We can use empty product to define ##a^0=1##.
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MTrying to understand why ##a^0 = 1## by using the positive-integer interpretation ##a \times a \times a \times \cdots## is the wrong...
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MMike_bb replied to the thread Undergrad Why ##a^0=1##?.For ##a^0=1## we have symmetry around ##a^0##: ##\frac{1}{a^{-1}} = a## ##\frac{a^1}{a^{-1}} = a \cdot a## For ##a^0\neq1## we don't...
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MMike_bb replied to the thread Undergrad Why ##a^0=1##?.Ah, that's what you're talking about. :smile:
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MWell, the first one is ##a\cdot a\cdot a\cdot a\cdot a##. So what's the third one? Or alternatively, note that the third one is...
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MMike_bb replied to the thread Undergrad Why ##a^0=1##?.I don't understand again. ##a\cdot a\cdot a\cdot a^2## ##a\cdot a\cdot a\cdot a^1## ##a\cdot a\cdot a\cdot a^0## What is the next step?
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MMike_bb replied to the thread Undergrad Why ##a^0=1##?.When you wrote post#2 you probably meant that "to multiply number by no a's" = ##a*a*a*a^0##. I can't understand how did you infer that...
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MMike_bb replied to the thread Undergrad Why ##a^0=1##?.I can't understand how does it work if ##x*x*x*x^0##? x³ = 1 × x × x × x x² = 1 × x × x x¹ = 1 × x x⁰ = 1 (we multiply by x zero...
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MWhat's the difference? Multiplication is commutative, you can write 1 wherever you want. My thought: you are overcomplicating things.
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MMike_bb replied to the thread Undergrad Why ##a^0=1##?.This seems logical to me. But after rereading, your second post confused me: How is it possible "to multiply number by no a's"? I...
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MEquation 1 has no solution: ##2^x > 0## for all ##x \in \mathbb{R}##. The only "value" satisfying ##2^x = 0## is ##x = -\infty##, which...
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MMike_bb replied to the thread Undergrad Why ##a^0=1##?.Hello! I decided to solve following equations: 1) Let ##2^x=0##: ##2^x=2^{2x}## and then ##x=0##. ##2^0=0## 2) Let ##2^x=1##...
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MMike_bb reacted to PeroK's post in the thread Undergrad Why should we need to re-prove theorems that have been proved already? with
Like.
Because the ones that haven't been proved are either unknown or too difficult. You could say the same about learning to program. Or... -
MMike_bb reacted to kuruman's post in the thread Undergrad Why should we need to re-prove theorems that have been proved already? with Like.
Also, so that we learn how to proceed in order to establish that something is correct. This is essential if the game is to acquire new...
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MMike_bb reacted to pasmith's post in the thread Undergrad Why should we need to re-prove theorems that have been proved already? with Like.
So that we understand the proofs, and can satisfy ourselves that they are indeed correct proofs. We don't take other people's word for...
