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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Alternate method for the summation of the given binomial sum
If $c_{0}, c_{1}, c_{2}, \ldots . . c_{15}$ are the binomial coefficients in the expansion of $(1+x)^{15}$, then the value of $\frac{c_{1}}{c_{0}}+2 \frac{c_{2}}{c_{1}}+3 \frac{c_{3}}{c_{2}}+\ldots+15 \frac{c_{15}}{c_{14}}$ is.
At first I was…
Orion_Pax
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Proof for Singularity of Additive Identity
On page 19 of his Calculus book, Apostol proves that $0$ is the only additive identity element for real numbers as follows:
In fact, if $0$ and $0'$ both have this property ($x+0=x$, $x+0'=x$ for all $x$ --op)
, then ${0+0' = 0}$ and $0+0=0$.…
Isaac Kleinman
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How to prove that some number is the minimum steps required to prove a certain logical statement?
Let's say we're working under the framework of classical logic, and I want to prove a statement by just using the laws of predicate logic (in which case we may define a step as an application of a single logical law), for example to prove…
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Proof, Golden Ratio and Fibonacci
I discovered a very interesting thing recently, and proved it by induction.
I found that the $n$th power of $\phi={1+\sqrt5 \over2}$, the Golden Ratio, is the product of $\phi$ with the $n$th Fibonacci number added to the $(n-1)$th Fibonacci…
DynamoBlaze
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Proof with Baire category theorem that the set $(0,1)$
i am searching for the proof that the interval $(0,1)$ is not countable by using the Baire category theorem.
Does someone know a book or has a reference for the proof ?
Thanks in advance.
McBotto.t
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Question regarding a proof for a subspace problem in Lang
$Statement\;of\;the\;Problem:$ Determine the dimension of the subspace of ${\mathbf{R^4}}$ consisting of all $X\in\mathbf{R^4}$ such that: $$x_1+2x_2=0 \;\;and\;\; x_3-15x_4=0$$
$My\;Question:$ Let $V=\mathbf{R^4}$ and $W=\mathbf{R^2}$. Let…
Johnq
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Is this proof by counterexample valid?
This is the given statement and its proof:
$$\exists m \in Z^+, \forall n \in Z^+, m
user137035
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Prove without method of contradiction that there exists a real number less than every positive real number that is positive
This question was asked before for proof by contradiction and which got me into thinking whether i could prove it without using a contradiction
Original problem statement is here
Prove by contradiction that a real number that is less than every…
ManZzup
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Give alternative proof of given theorem (relates to inverses of functions) need to use (b,a)∈ $B\times A.$
I have no idea of how to do this. We need to create an alternative proof using some of the ideas on the bottom, but I'm lost. Any ideas on how to do this? I'm not sure how to even start the problem...
We are asked to use the following strategy to…
ffry
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Validity of "circular" proofs
I believe this is an easy question.
I put circular in quotations because I'm pretty sure I'm not talking about circular proofs in general.
I was thinking about how to prove that any function whose derivative is 0 for any $x$ is a constant function.…
Luka Horvat
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Direct understanding of vector projection
I'm aware that we can project an arbitrary vector $v$ onto a unit vector $\hat{\mathbf{k}}$ by $(\mathbf{v} \cdot \hat{\mathbf{k}})\hat{\mathbf{k}}$
But why is this true?
I would imagine that such a clean result has a correspondingly clean…
P i
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$n!\sum_{k=1}^n \frac{a_{k}}{k!}$ is always integer.
$\displaystyle n!\sum_{k=1}^n \frac{a_{k}}{k!}\in \mathbb{Z}$
where
$n,a_k$
and $k$ are integers. I know the proof by induction. Is there any other technique to prove it?
Thank you.
Silent
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How can I prove $a^2 +b^2 >2ab$ only with Natural numbers?
I need to show $a^2 +b^2 > 2ab$ , but only with natural numbers, for that reason, I can't use negative numbers, the zero, or others non-natural numbers, e.g. I can't use the fact $(a-b)^2 > 0$
Jorge S.
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Let $E$ an $\mathbb{R}$-vectorial space and $f : E \rightarrow E $ an endomorphism. Prove that...
Let $E$ an $\mathbb{R}$-vectorial space and $f : E \rightarrow E $ an endomorphism. Prove that:
$(a)$ $dim (E)$ odd $\Rightarrow$ $f$ has at least one eigenvalue.
$(b)$ $dim (E)$ pair and $det(f) < 0 $ $\Rightarrow$ $f$ has at least two different…
Spectree
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