If there is a fault in the logic, please explain it in simple terms.
Thank you.
2026-03-27 03:41:45.1774582905
Is this proof by contradiction that 9+13√3 is irrational correct?
671 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in PROOF-VERIFICATION
- how is my proof on equinumerous sets
- Existence of a denumerble partition.
- Confirmation of Proof: $\forall n \in \mathbb{N}, \ \pi (n) \geqslant \frac{\log n}{2\log 2}$
- Calculating probabilities using Markov chains.
- Solution to a hard inequality
- Given a function, prove that it's injective
- Is the following set open/closed/compact in the metric space?
- Surjective function proof
- Possible Error in Dedekind Construction of Stillwell's Book
- Proving dual convex cone property
Related Questions in IRRATIONAL-NUMBERS
- Convergence of a rational sequence to a irrational limit
- $\alpha$ is an irrational number. Is $\liminf_{n\rightarrow\infty}n\{ n\alpha\}$ always positive?
- Is this : $\sqrt{3+\sqrt{2+\sqrt{3+\sqrt{2+\sqrt{\cdots}}}}}$ irrational number?
- ls $\sqrt{2}+\sqrt{3}$ the only sum of two irrational which close to $\pi$?
- Find an equation where all 'y' is always irrational for all integer values of x
- Is a irrational number still irrational when we apply some mapping to its decimal representation?
- Density of a real subset $A$ such that $\forall (a,b) \in A^2, \ \sqrt{ab} \in A$
- Proof of irrationality
- Is there an essential difference between Cartwright's and Niven's proofs of the irrationality of $\pi$?
- Where am I making a mistake in showing that countability isn't a thing?
Related Questions in RATIONALITY-TESTING
- Irrationality of $\log_2(2015)$
- Find an equation where all 'y' is always irrational for all integer values of x
- What is Euler doing?
- Is there an essential difference between Cartwright's and Niven's proofs of the irrationality of $\pi$?
- $\sqrt{\frac{\pi e}{2}}=\frac{1}{1+\mathrm{K}_{i=1}^{\infty}{\frac{i}{1}}}+\sum_{n=0}^{\infty}{\frac{1}{(2n+1)!!}}$ implies $\sqrt{\pi e/2}\notin Q$?
- Rationality of circumference of an ellipsis with rational semi-axes
- Rationality of the Gamma function
- Can we find smallest positive $x$ such that $\pi^x$ is rational?
- For the expression $\sqrt{\frac{x}{y}}$ to be rational, is it necessary for both to be squares?
- Spivak Calculus 4-th Ed., Chapter 2, Exercise 13a, Understanding the proof of $\sqrt3$ being irrational.
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
Although there is no problem with the logic, you are assuming that $\sqrt 3$ is irrational. I don't think this is what you were intended to do, since showing that $\sqrt 3$ is irrational would be the most difficult step in the proof.