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Hilbert’s Hotel Mapping Calculator — result sheet
Explore finite guest shifts and the classic countably infinite room mappings used to explain Hilbert’s hotel thought experiment.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: One guest: old room n→n+1; finite block of m guests: old room n→n+m; countably infinite block: old guest n→2n and new guest k→2k−1.
Hilbert’s hotel is a thought experiment about countably infinite sets, not a finite hotel booking tool. The finite modes show how a shift makes room for one or a finite block of new guests. The countably-infinite mode displays the even/odd mapping that leaves every positive integer room assigned while making room for another countable list. No physical hotel, capacity claim, or real-world reservation is implied.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Mapping scenario — 3 choices
- Existing guests in finite demonstration — guests; minimum 1; maximum 1000000
- New guests in finite scenarios — guests; minimum 1; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Mapping scenario | one-new-guest |
| Existing guests in finite demonstration | 20 |
| New guests in finite scenarios | 5 |
For one new guest, each existing guest shifts from room n to n+1; the new guest takes room 1 and rooms 1–21 are assigned in the finite demonstration.
Assumptions and limits
- Room and guest labels begin at 1 and are positive integers.
- Finite modes use the entered demonstration counts and show a shift of existing guests.
- The countably-infinite mode treats both lists as countably infinite and uses an abstract bijection.
- The finite demonstration counts do not approximate the cardinality of infinity.
- The mapping describes room labels only; it does not model time, moving cost, accessibility, or real lodging operations.
- The result is an educational set-mapping illustration, not a practical occupancy or scheduling recommendation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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