```json
{
  "infinity": {
    "symbol": "∞",
    "types": {
      "countable": {
        "description": "The size of the set of natural numbers.",
        "example": "Natural numbers (1, 2, 3, ...)",
        "cardinality": "ℵ₀"
      },
      "uncountable": {
        "description": "The size of the set of real numbers.",
        "example": "Real numbers (all decimal expansions)",
        "cardinality": "2^ℵ₀"
      }
    },
    "applications": [
      {
        "field": "Calculus",
        "usage": "Limits, integrals, and derivatives."
      },
      {
        "field": "Set Theory",
        "usage": "Understanding different sizes of infinity."
      },
      {
        "field": "Physics",
        "usage": "Concepts like infinite density in black holes."
      }
    ],
    "properties": {
      "non-numeric": true,
      "cannot_be_reached": true,
      "conceptual": true
    }
  }
}

```