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Data Science & AIparcadei

continuity

Problem-solving strategies for continuity in real analysis

Stars
3,795
Source
parcadei/Continuous-Claude-v3
Updated
2026-01-26
Slug
parcadei--Continuous-Claude-v3--continuity
View on GitHubRaw SKILL.md

// install — copy + paste into any project

mkdir -p .claude/skills && curl -fsSL https://raw.githubusercontent.com/parcadei/Continuous-Claude-v3/HEAD/.claude/skills/math/real-analysis/continuity/SKILL.md -o .claude/skills/continuity.md

Drops the SKILL.md into .claude/skills/continuity.md. Works with Claude Code, Cursor, and any agent that loads SKILL.md files from .claude/skills/.

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

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

Sympy_Limit_Left

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

Z3_Prove

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.