All Questions
4
questions
-2
votes
2
answers
260
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For any numbers $a, b,$ and $c,$ $a + b = a + c$ if and only if $b = c$ [duplicate]
I was reading about the field of real numbers $\mathbb{R},$ and a basic question arose in my mind.
How one should prove that, for any numbers $a, b,$ and $c,$ $a + b = a + c$ if and only if $b = c?$
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- 3,794
1
vote
2
answers
68
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Help with a proof of a consequence from the axioms of addition and multiplication
While reading through Analysis 1 by Vladimir A. Zorich, I encountered this proof which has this 1 step I can't understand. Here is the consequence and the proof:
For every $x\in \mathbb R$ the ...
- 537
0
votes
0
answers
176
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Question of proof of archimedean property
For every real number x there exists an integer $n$ such that $n>x$.
The book is using contradiction,
Suppose $x$ is a real number such that $n≤x$ for every $n$,that mean $x$ is the upper bound ...
user743730
1
vote
1
answer
105
views
Proof of |x · y| = |x| · |y| using axioms of real numbers
I'm trying to prove |x · y| = |x| · |y| using only the axioms of real numbers. I'm using the definition of the modulus function to be below. I thought I should start by distinguishing four cases like (...
user378721