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Prove or Disprove: for All Integers a,b, if ab and ba, then a=ba , b \text {, if } a \mid b \text { and } b \mid a \text {, then } a = b \text {. }

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Prove or disprove: For all integers a,b, if ab and ba, then a=ba , b \text {, if } a \mid b \text { and } b \mid a \text {, then } a = b \text {. }


Definitions:

Growth Rate

A measure of the increase in size, number, value, or strength of something over a specific period of time.

Beta

An indicator of the degree to which a particular stock's movement is volatile compared to the general market, conveying the risk level of the stock relative to the market norm.

Risk-Free Rate

A return on an investment that is guaranteed not to result in financial loss, usually tied to state bonds.

Expected Return

The anticipated profit or loss from an investment, taking into consideration the potential outcomes and their probabilities.

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