continuity

Name: continuity
Availability: InStock
Author: parcadei

Verify continuity conditions using SymPy limits and Z3 proofs.

3.9k|296|Updated Dec 23, 2025

Search Tags:#real analysis #calculus #continuity #z3 #limit #sympy

Ready to run

npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill continuity-parcadei

💬 Prompt for ChatGPT / Claude Chat▼

Please help me install this Agent Skill.
Skill: continuity
Source: https://github.com/parcadei/Continuous-Claude-v3/tree/main/.claude/skills/math/real-analysis/continuity
Command: npx skills add https://github.com/parcadei/Continuous-Claude-v3 --skill continuity-parcadei

SYSTEM DOCUMENTATION & REQUIREMENTS

💡 This Skill requires sympy, z3, and includes scripts (resource) and references (resource) components.

What problem does it solve?

This Skill provides a structured approach to solving continuity problems in real analysis, ensuring all necessary conditions are checked and leveraging computational tools for verification.

Core Features & Use Cases

Definition Checklist: Guides users through the three essential conditions for continuity at a point.
Limit Computation: Integrates with SymPy to symbolically compute limits, including one-sided limits.
Formal Verification: Supports using Z3 for proving continuity properties.
Use Case: When faced with a piecewise function and asked to determine if it's continuous at a specific point, this skill will guide you to check the function's value, the limit's existence, and their equality, using SymPy for the limit calculation.

Quick Start

Use the continuity skill to check if the function f(x) = x^2 is continuous at x=2.

Frequently Asked Questions about continuity

High-intent search queries and answers about installing and using this skill.

FAQPage Schema

How do I check if a piecewise function is continuous at a specific point?▼

To verify continuity at a specific point, check the function definition, confirm the limit exists, and ensure the limit equals the function value using SymPy for symbolic computation and Z3 for formal proofs.

What are the three conditions required to prove real analysis continuity?▼

Real analysis continuity requires the function to be defined at the point, the limit to exist at that point, and the limit to equal the function value. This Skill uses a structured checklist to verify all three conditions.

Can I use SymPy to compute one-sided limits for calculus problems?▼

Yes, you can use SymPy to compute one-sided limits for calculus problems. This Skill integrates SymPy for symbolic limit computation to handle one-sided limits when verifying continuity in real analysis.

Does Z3 work with SymPy for proving continuity properties in real analysis?▼

Yes, Z3 works with SymPy for proving continuity properties in real analysis. This Skill integrates SymPy for symbolic limit calculation and Z3 for formal verification of continuity conditions.

What's the best way to solve real analysis continuity problems with piecewise definitions?▼

The best way to solve real analysis continuity problems with piecewise definitions is to systematically verify the function value, check limit existence, and confirm their equality using SymPy and Z3 for computational verification.