WHAT A KIDDER!!! Ha! Ha!
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You can't just assume things.
You can assume things. It's called an axiom.You don't need it though. The usual axioms for the definition of multiplication over the natural numbers are:
- Base case: 0 × k = 0
- Inductive case: (i + 1) × k = (i × k) + k
That 1×1=1 follows naturally if you choose k=1. (Note also that the above can be written using Peano arithmetic, which constructs things using very few basic concepts.) The proof of associativity and commutativity of multiplication are left as exercises.
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Prove that part. You can't just assume things.
I was going to assume this was a joke, but damnit! I can't.So do you want me to prove the definition of multiple, or the definition of 1 as the neutral element of multiplication?
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I was going to assume this was a joke, but damnit! I can't.
I had a geometry teacher that kept telling me never to make assumptions no matter what. Then I had a discrete mathematics teacher who would prove complex equations by writing "CLEARLY" as the entire body of the proof.
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I had a geometry teacher that kept telling me never to make assumptions no matter what. Then I had a discrete mathematics teacher who would prove complex equations by writing "CLEARLY" as the entire body of the proof.
That's not making an assumption. It's just being able to see more complex logic quickly. Unless he was wrong or just guessing. It's very important to know your audience for a proof. Seems like you weren't in his idea of who his audience was or should have been.
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I had a discrete mathematics teacher who would prove complex equations by writing "CLEARLY"
Your math teacher was Norbert Wiener? (Google tip for the uneducated: look up norbert wiener "it is obvious")
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all of the digits in the bottom row are multiples of one.
As opposed to all the digits which aren't.
Edit: OK, need to stop replying to posts made during my vacation, especially before I finish reading them.
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Received that error again
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Useful feature:
Kept me from going "I don't remember this, what is @Luhmann talking about?" Stop trying to abort system tasks or do a nice necro and fill in context so we don't need to reread.
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I have to admit I grudgingly like that feature.
Now if only the basic shit worked.
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Off those options I clearly went with: necro an old topic and have everybody wonder what I was talking about.
You're welcome!
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I scrolled up a bit, saw another kind of @error, and assumed this would be an old thread.