User Guide

Final Equation User Guide

Welcome to Final Equation - the interactive platform for learning and practicing formal mathematical proofs. This guide covers the Android and iOS mobile applications. While there may be slight differences between platforms, the core functionality is the same.

Getting Started

After downloading the app, create an account or sign in. You'll be taken to the Home screen where you can access all features of the application.

Natural Number Game

The Natural Number Game is an interactive tutorial that teaches you how to write formal mathematical proofs. It's the perfect starting point for beginners and a great refresher for experienced users.

How It Works

  • Structured Levels: Progress through carefully designed worlds, each introducing new concepts and tactics.
  • Interactive Proofs: Write proofs by applying tactics to transform your goal step by step.
  • Instant Feedback: See immediately whether your tactic worked and how it changed the proof state.
  • No Prior Experience Required: The game starts from the basics and builds up gradually.

Game Interface

  • Goal Panel: Shows what you need to prove.
  • Hypotheses Panel: Shows what facts you have available.
  • Tactic Input: Where you enter tactics to progress the proof.
  • Tactic Palette: Quick-access buttons for common tactics.

Proof Editor

The Proof Editor is where you construct formal mathematical proofs. It provides a powerful environment for working with theorems and lemmas.

Proof Interface

  • Goal Display: Shows your current proof obligations - what remains to be proven.
  • Context/Hypotheses: Lists all available assumptions and previously proven facts.
  • Tactic Input: Enter tactics to transform and complete your proof.
  • Tactic Suggestions: Intelligent recommendations based on your current goal.

Common Tactics

  • intro: Introduce a hypothesis or variable.
  • apply: Apply a theorem or hypothesis to the goal.
  • exact: Provide an exact term that matches the goal.
  • rw (rewrite): Rewrite using an equality.
  • induction: Perform induction on a natural number.
  • cases: Split into cases based on a hypothesis.
  • simp: Simplify the goal using known lemmas.
  • ring: Solve equations in a ring (arithmetic).

Getting Help

When you're stuck, tap the "Hint" or "Suggestions" button to see recommended tactics. The system analyzes your current goal and provides contextually relevant suggestions.

Collaborative Proofs

Work together with others on proofs in real-time. This feature is perfect for study groups, classroom activities, or getting help from the community.

Starting a Collaboration Session

  1. Open a proof you want to work on.
  2. Tap the "Collaborate" or share icon.
  3. Share the session link with others, or invite users directly.

During Collaboration

  • Real-time Updates: See changes made by others instantly.
  • Participant List: View who is currently in the session.
  • Chat: Discuss strategies and ideas with collaborators.
  • Turn-based or Free-form: Choose how to coordinate contributions.

Home / Timeline

The Timeline is your social feed for mathematical discussions and shared content.

What Appears in Your Timeline

  • Posts authored by you.
  • Posts from users you follow.
  • Posts containing hashtags you subscribe to.
  • System announcements and notifications.

Interacting with Posts

  • Reply: Respond to a post with your own message.
  • Like: Show appreciation for helpful content.
  • Share: Spread interesting posts to your followers.

Message Editor

Create posts that combine text and mathematical expressions. The Message Editor provides a specialized keyboard for mathematical input.

Math Keyboard Features

  • Mode Toggle (A/∑): Switch between text and math input modes.
  • Display Mode (T/D): Toggle between inline and display math formatting.
  • Navigation Arrows: Move cursor through complex expressions.
  • Symbol Palettes: Access Greek letters, operators, relations, and more.

Available Symbol Categories

  • Greek letters (α, β, γ, π, Σ, etc.)
  • Mathematical operators (+, -, ×, ÷, etc.)
  • Relations (=, ≤, ≥, ≈, ≡, etc.)
  • Set notation (∈, ⊂, ∪, ∩, etc.)
  • Logic symbols (∧, ∨, ¬, ∀, ∃, etc.)
  • Arrows (→, ←, ↔, ⇒, etc.)
  • Fractions, roots, superscripts, subscripts.

Creating Structures

  • Fractions: Create numerator/denominator structures.
  • Roots: Square roots and nth roots.
  • Subscripts/Superscripts: For indices and exponents.
  • Matrices: Create tables and matrices.
  • Fenced Expressions: Parentheses, brackets, braces with automatic sizing.

User Profile

Your profile displays your information and activity. Access it by tapping any avatar or through the menu.

Profile Information

  • Display name and username.
  • Bio/description.
  • Follower and following counts.
  • Your recent posts and proofs.
  • Achievements and progress.

Editing Your Profile

Tap the edit button on your profile to update your display name, bio, and avatar image.

Subscriptions

Follow users and topics to customize your timeline.

Finding Users

  • Search by username (minimum 3 characters).
  • Search by full name (minimum 3 characters).
  • Search by exact email address.

Following Topics

Subscribe to hashtags to see all posts containing those tags. Trending topics are displayed based on recent activity.

Settings

Configure the application to suit your preferences.

Available Settings

  • Location Sharing: Attach your location to posts (on/off).
  • Cache Management: Set cache size limits and clear cached data.
  • Font Scaling: Adjust text size for readability.
  • Notifications: Configure push notification preferences.
  • Theme: Choose light or dark mode (where available).

Account Management

Account Deletion

You can permanently delete your account and all associated data at any time. Visit Account Deletion on our website or access it through the app settings. This action cannot be undone.

Privacy

Review our Privacy Policy for details on how we handle your data.

Getting Help

If you encounter issues or have questions:

  • Check this user guide for answers.
  • Ask the community by posting with #help.
  • Contact support at support@finalequation.com.

Tips for Success

  • Start with the Natural Number Game: It's the best way to learn proof techniques.
  • Practice regularly: Like any skill, proving theorems improves with practice.
  • Don't be afraid to ask: The community is here to help.
  • Read others' proofs: Learn different approaches and techniques.
  • Collaborate: Working with others accelerates learning.