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continuity

Problem-solving strategies for continuity in real analysis

Packaged view

This page reorganizes the original catalog entry around fit, installability, and workflow context first. The original raw source lives below.

Stars
3,611
Hot score
99
Updated
March 20, 2026
Overall rating
C4.8
Composite score
4.8
Best-practice grade
B81.2

Install command

npx @skill-hub/cli install parcadei-continuous-claude-v3-continuity

Repository

parcadei/Continuous-Claude-v3

Skill path: .claude/skills/math/real-analysis/continuity

Problem-solving strategies for continuity in real analysis

Open repository

Best for

Primary workflow: Ship Full Stack.

Technical facets: Full Stack.

Target audience: everyone.

License: Unknown.

Original source

Catalog source: SkillHub Club.

Repository owner: parcadei.

This is still a mirrored public skill entry. Review the repository before installing into production workflows.

What it helps with

  • Install continuity into Claude Code, Codex CLI, Gemini CLI, or OpenCode workflows
  • Review https://github.com/parcadei/Continuous-Claude-v3 before adding continuity to shared team environments
  • Use continuity for development workflows

Works across

Claude CodeCodex CLIGemini CLIOpenCode

Favorites: 0.

Sub-skills: 0.

Aggregator: No.

Original source / Raw SKILL.md

---
name: continuity
description: "Problem-solving strategies for continuity in real analysis"
allowed-tools: [Bash, Read]
---

# Continuity

## When to Use

Use this skill when working on continuity problems in real analysis.

## Decision Tree


1. **Check Definition**
   - f(a) exists (function defined at point)
   - lim_{x->a} f(x) exists
   - lim_{x->a} f(x) = f(a)

2. **Use SymPy for Limit Check**
   - `sympy_compute.py limit "f(x)" --var x --at a`
   - Compare with f(a)

3. **Piecewise Functions**
   - Check left and right limits separately
   - `sympy_compute.py limit "f(x)" --var x --at a --dir left`

4. **Verify with Z3**
   - `z3_solve.py prove "limit_exists implies continuous"`


## Tool Commands

### Sympy_Limit
```bash
uv run python -m runtime.harness scripts/sympy_compute.py limit "f(x)" --var x --at a
```

### Sympy_Limit_Left
```bash
uv run python -m runtime.harness scripts/sympy_compute.py limit "f(x)" --var x --at a --dir left
```

### Z3_Prove
```bash
uv run python -m runtime.harness scripts/z3_solve.py prove "continuous_at_a"
```

## Cognitive Tools Reference

See `.claude/skills/math-mode/SKILL.md` for full tool documentation.
continuity | SkillHub