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Problem-solving strategies for continuity in real analysis

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@parcadeiparcadei@parcadei
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continuous-claude-v3
3.9k156 skills32 agents

Claude Code

$ npx -y skills add parcadei/Continuous-Claude-v3 --skill continuity --agent claude-code

SKILL.md

continuity.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

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.

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Repo: parcadei/Continuous-Claude-v3

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A persistent, learning, multi-agent development environment built on Claude Code Continuous Claude transforms Claude Code into a continuously learning system that maintains context across sessions, orchestrates specialized agents, and eliminates wasting

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Questions about continuity.

Which coding agents can use continuity?
continuity installs in Claude Code, Codex, Cursor, Gemini CLI, GitHub Copilot, OpenCode and Windsurf with the skills CLI, using each agent's flag shown on this page. Flowy's auto-invocation, which fires a skill when your prompt matches, runs in Claude Code only.