This page is a sub-page of our page on Numbers.
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Related KMR pages:
• Numbers and their Digits in different Bases.
• Representation and Reconstruction of Numbers.
• Shift of Basis (in general).
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Other sources of related information:
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Experiment here with computing the Digits of a Number with respect to different Bases.
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The Base-Shift formula for Numbers
It is often useful to have a symbolic name for the operation of shifting the \, B_{ase} \, of a \, n_{umber} \, from \, {B_{ase}}_1 \, to \, {B_{ase}}_2 \,. This operation will be called \, B_{aseShift} \, and its action on a given \, n_{umber} \, will be written in three different ways:
i) \, {[B_{aseShift}]}_{{B_{ase}}_2}^{{B_{ase}}_1} \; , or
ii) \, {[n_{umber}]}_{{B_{ase}}_2}^{{B_{ase}}_1} \; , if the \, B_{aseShift} \, operation is clear from the context, or
iii) \, {[\,\,\,]}_{{B_{ase}}_2}^{{B_{ase}}_1} \; , if both the \, n_{umber} \, and the \, B_{aseShift} \, operation are clear from the context.
A Base-Shift Diagram for Numbers:
Numbers are naturally related to Music:
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