The Missing Rung
Meditations on Oneness
Local folio mark · 111
Page 1 · Descend the product ladder
Luna's descending record
In an Archive field note, Luna fixes a nonzero real number . She lets be the product of copies of :
Every neighboring pair follows the same rule: .
Complete the ladder
Write on the missing rung. Use scratch paper for the proof.
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A missing rung lies below . Find the only value of that lets the same neighboring-rung rule hold at . Explain exactly where the condition is used.
Page 2 · Follow two echoes
Powers and empty products
We write .
For , the quotient rule is .
The product of a whole list equals the product of its left block times the product of its right block.
Two views of the same one
Use separate paper for your explanations.
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What must mean? Then check in two ways: as a nonzero number divided by itself, and using the exponent-division rule.
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To preserve the product-splitting rule when one block contains no factors, what must the product of the empty block be? Prove that no other value works.
Zero factors do not erase a product. They leave multiplication ready to begin.