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J W
J W
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I want to build a factory and I go to a bank for a loan, to finance part of the investment cost.

Bankers tend to think in $a:b$: "How many euros we will lend for every euro the compnaycompany will invest". And they tend to have rules of thumb on the matter, say a $3:1$ rule. From the point of view of the company, this could be written $1:3$ and here, confusion may arise more easily, because "$1/3$" should be interpreted as "the compnaycompany will invest one third of what the bank will lend" and not as "one third of the total cost of the factory".

To arrive at this last magnitude the relation is always $a:b \rightarrow \frac {a}{a+b}$

More generally, I think a fraction $a/b$ (which then can be written also as a number, a decimal, etc), is meanigfullmeaningful only when $a$ and $b$ measure same entities in nature (in my example, money in the same currency). But the concept represented usually by $a:b$ can bring together items that are not alike (say, "$a$ car-accident deaths per $b$ kilometers of highways), in which case there is no meaningful interpretation of $a+b$.

I want to build a factory and I go to a bank for a loan, to finance part of the investment cost.

Bankers tend to think in $a:b$: "How many euros we will lend for every euro the compnay will invest". And they tend to have rules of thumb on the matter, say a $3:1$ rule. From the point of view of the company, this could be written $1:3$ and here, confusion may arise more easily, because "$1/3$" should be interpreted as "the compnay will invest one third of what the bank will lend" and not as "one third of the total cost of the factory".

To arrive at this last magnitude the relation is always $a:b \rightarrow \frac {a}{a+b}$

More generally, I think a fraction $a/b$ (which then can be written also as a number, a decimal, etc), is meanigfull only when $a$ and $b$ measure same entities in nature (in my example, money in the same currency). But the concept represented usually by $a:b$ can bring together items that are not alike (say, "$a$ car-accident deaths per $b$ kilometers of highways), in which case there is no meaningful interpretation of $a+b$.

I want to build a factory and I go to a bank for a loan, to finance part of the investment cost.

Bankers tend to think in $a:b$: "How many euros we will lend for every euro the company will invest". And they tend to have rules of thumb on the matter, say a $3:1$ rule. From the point of view of the company, this could be written $1:3$ and here, confusion may arise more easily, because "$1/3$" should be interpreted as "the company will invest one third of what the bank will lend" and not as "one third of the total cost of the factory".

To arrive at this last magnitude the relation is always $a:b \rightarrow \frac {a}{a+b}$

More generally, I think a fraction $a/b$ (which then can be written also as a number, a decimal, etc), is meaningful only when $a$ and $b$ measure same entities in nature (in my example, money in the same currency). But the concept represented usually by $a:b$ can bring together items that are not alike (say, "$a$ car-accident deaths per $b$ kilometers of highways), in which case there is no meaningful interpretation of $a+b$.

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Alecos Papadopoulos
Alecos Papadopoulos
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I want to build a factory and I go to a bank for a loan, to finance part of the investment cost.

Bankers tend to think in $a:b$: "How many euros we will lend for every euro the compnay will invest". And they tend to have rules of thumb on the matter, say a $3:1$ rule. From the point of view of the company, this could be written $1:3$ and here, confusion may arise more easily, because "$1/3$" should be interpreted as "the compnay will invest one third of what the bank will lend" and not as "one third of the total cost of the factory".

To arrive at this last magnitude the relation is always $a:b \rightarrow \frac {a}{a+b}$

More generally, I think a fraction $a/b$ (which then can be written also as a number, a decimal, etc), is meanigfull only when $a$ and $b$ measure same entities in nature (in my example, money in the same currency). But the concept represented usually by $a:b$ can bring together items that are not alike (say, "$a$ car-accident deaths per $b$ kilometers of highways), in which case there is no meaningful interpretation of $a+b$.