If you already have a proof for some result but want to ask for a different proof (using different methods).
Questions tagged [alternative-proof]
3599 questions
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Alternative metric space proof for $d(x,y)\geq 0$
Wikipedia describes a metric space as $(M,d)$, where $M$ is a set and $d(x,y)$ is a metric. The axioms are as follows:
$d : M \times M \rightarrow \mathbb{R}$
$d( x, x) = 0$
$d( x, y ) = d ( y, x )$
$d( x, z ) \leq d( x, y ) + d( y , z )$
A proof of…
Patrick Browne
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Calculus proof - Possible application of a known proof
Let $a_n < c < b_n$ and $a_n, b_n → c$ as $n → ∞ $.
Suppose $ f : \mathbb{R} → \mathbb{R} $ is continuous.
Show that (Possibly using similar proof to FTC...?)
$$ \lim_{n \to\infty }\frac{1}{{b_n -…
jimmy_thomas33
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Proving the circumradius (R) for an equilateral triangle
I am intrigued about how people would go about proving the formula for the circumradius in the image above. I went about it by using the cosine rule and it worked out nicely. Any other methods?
Jamminermit
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How to check if a function is injective and surjective
I'm currentlly doing a course in abstract algebra and I often have to prove a map is surjective or injective. It's always done the same way, we take $f(a)=f(b)$ and deduce $a=b$, or we show that for every $y$ in the range there is an element x in…
Lowkey
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Can I derive the sum of squares formula without induction and through the formula for series?
I have $1^2+2^2+...+n^2$ and I want to prove the sum is $\frac{m(m+1)(2m+1)}{6}$. So for proving the formula for $1+3+5+7+... = n^2$ this is how i got the formula:
the common difference is 2, so the formula for $a_n = 2n-1$
The sum of an arithmetic…
user8290579
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Prove the following statement using two methods of proof: If $n$ and $m$ are non-zero integers, then $n^2-m^2≠1$.
I have already seen the proof by contradiction for this problem, but I can't figure out any other way to prove it. This was on a test, so far we have only learned direct method of proof, contrapositive method, contradiction method, and briefly cases…
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Fredholm Integral Operator - Arzela-Ascoli Theorem
I know how to prove that the Fredholm Integral operator $$ T_k : L^2([0,1]) \rightarrow L^2([0,1]) \; \left(T_kf \right)(s)= \int_{[0,1]} k(s,t) \, f(t) \; dt$$ with $$k \in L^2([0,1]^2) \; , f\in L^2([0,1])$$is compact. I use the fact that the…
McBotto.t
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Are there other proofs of Fermat's theorem other than Wiles?
Andrew Wiles proved Fermat's last theorem in 1994, 23 years ago. I studied the proof, and I was wondering if anyone have provided a shorter proof or even shortcuts since then?
Tal-Botvinnik
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How to show that there are countably many Turing machines?
There is a natural way to prove that there are countable many Turing machines. First we will encode the Turing machines with binary string and than by setting a bijection from set of all encodings of Turing machines to set Natural numbers , this…
user275490
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Is there an intuitive reason that explains Fermat's Last Theorem?
In number theory, Fermat's Last Theorem (or Fermat's conjecture) states that no three positive integers a, b, and c satisfy the equation $a^n + b^n = c^n$ for any integer value of $n$ greater than 2.
I know that there are math intensive proofs for…
zhirzh
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How to prove $\sum_{i=1}^{n} i = \frac{n}{2}(n+1)$ without words?
Possible Duplicate:
Proof for formula for sum of sequence $1+2+3+\ldots+n$?
Is there a picture proof for $\sum_{i=1}^{n} i = \frac{n}{2}(n+1)$?
Lori Jiang
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Find at least ten different prime numbers $p$ such that $p + 6$ is also prime.
How can I find the set of prime numbers without using the direct trial and error?
