I tried to prove the ff:
If x^2 is an irrational number then x is an irrational number.
Is there another way of proving the statement by contraposition, without using the closure property of the set of rational numbers under multiplication?
2026-04-28 12:16:29.1777378589
Proof by Contrapositive (without using the closure property )
60 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in LOGIC
- Theorems in MK would imply theorems in ZFC
- What is (mathematically) minimal computer architecture to run any software
- What formula proved in MK or Godel Incompleteness theorem
- Determine the truth value and validity of the propositions given
- Is this a commonly known paradox?
- Help with Propositional Logic Proof
- Symbol for assignment of a truth-value?
- Find the truth value of... empty set?
- Do I need the axiom of choice to prove this statement?
- Prove that any truth function $f$ can be represented by a formula $φ$ in cnf by negating a formula in dnf
Related Questions in ALTERNATIVE-PROOF
- Are $[0,1]$ and $(0,1)$ homotopy equivalent?
- An isomorphism $f:G_1 \to G_2$ maps the identity of $G_1$ to the identity of $G_2$
- Simpler Derivation of $\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}$,
- inequality with arc length integral
- In how many ways can the basketball be passed between four people so that the ball comes back to $A$ after seven passes? (Use recursion)
- Deriving the gradient of the Augmented Lagrangian dual
- An irreducible Markov chain cannot have an absorbing state
- Clarifying a proof that a certain set is an algebra
- Dilogarithmic fashion: the case $(p,q)=(3,4)$ of $\int_{0}^{1}\frac{\text{Li}_p(x)\,\text{Li}_q(x)}{x^2}\,dx$
- Proof by contrapositive: $x^4 + 2x^2 - 2x \lt 0 \Rightarrow 0 \lt x \lt 1$
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?