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.
Install command
npx @skill-hub/cli install parcadei-continuous-claude-v3-continuity
Repository
Skill path: .claude/skills/math/real-analysis/continuity
Problem-solving strategies for continuity in real analysis
Open repositoryBest 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
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.