how can i prove this?
$\forall n \exists p (p^2 \leq n <(p+1)^2)$
The domain of quantifiers is N.
It came from discrete mathematics, and I don't know how to start proofing.
2026-03-31 21:09:26.1774991366
proof $\forall n \exists p (p^2 \leq n <(p+1)^2)$
63 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in NUMBER-THEORY
- Maximum number of guaranteed coins to get in a "30 coins in 3 boxes" puzzle
- Interesting number theoretical game
- Show that $(x,y,z)$ is a primitive Pythagorean triple then either $x$ or $y$ is divisible by $3$.
- About polynomial value being perfect power.
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Reciprocal-totient function, in term of the totient function?
- What is the smallest integer $N>2$, such that $x^5+y^5 = N$ has a rational solution?
- Integer from base 10 to base 2
- How do I show that any natural number of this expression is a natural linear combination?
- Counting the number of solutions of the congruence $x^k\equiv h$ (mod q)
Related Questions in DISCRETE-MATHEMATICS
- What is (mathematically) minimal computer architecture to run any software
- What's $P(A_1\cap A_2\cap A_3\cap A_4) $?
- The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$
- Given is $2$ dimensional random variable $(X,Y)$ with table. Determine the correlation between $X$ and $Y$
- Given a function, prove that it's injective
- Surjective function proof
- How to find image of a function
- Find the truth value of... empty set?
- Solving discrete recursion equations with min in the equation
- Determine the marginal distributions of $(T_1, T_2)$
Related Questions in PROOF-WRITING
- how is my proof on equinumerous sets
- Do these special substring sets form a matroid?
- How do I prove this question involving primes?
- Total number of nodes in a full k-ary tree. Explanation
- Prove all limit points of $[a,b]$ are in $[a,b]$
- $\inf A = -\sup (-A)$
- Prove that $\sup(cA)=c\sup(A)$.
- Supremum of Sumset (Proof Writing)
- Fibonacci Numbers Proof by Induction (Looking for Feedback)
- Is my method correct for to prove $a^{\log_b c} = c^{\log_b a}$?
Related Questions in NATURAL-NUMBERS
- Recursive Induction Floor Proof Help
- Countable set example
- Bound a natural by two consecutive powers
- Set theory that proves that if its consistient, is only proves true things about arithmetic
- $n$ is natural number. What is the result of $(-1)^{2n}-(-1)^{4n-1}-1^{n+1}-(-2)^3$
- Given a sufficiently large integer $N$, is it true that there are more primes than perfect squares in $[1,N]$?
- How to show that $(S\cup\{0\},\ge)$ is order-isomorphic to $(S,\ge)$?
- Some questions about the successor function
- What IS the successor function without saying $S(n) = n + 1$?
- Prove addition is commutative using axioms, definitions, and induction
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?
If $n$ is a perfect square we can take $p=\sqrt{n}$. If not let $p$ be the largest natural number for which $p^2 < n$. Then $n < (p+1)^2$, since otherwise we get a contradiction on the maximality of $p$.