Interest rate floor value

Excellearner used Ask the Experts™
All, I am preparing for MFE (financial engineering). I could not thin of any other forum where i could seek help for clearing my doubts on financial products.

Dear experts, is my below understanding correct?

Is  r>-1  coming from this statement?

&&&1 + r&&&

if 1+r>0, then r>-1

Extract from Stochastic Calculus for Finance 1

We introduce also an interest rate 1^n. One dollar invested in the money

market at time zero will yield 1 + r dollars at time one. Conversely, one dollar

borrowed from the money market at time zero will result in a debt of &&&1 + r&&&

at time one. In particular, the interest rate for borrowing is the same as the

interest rate for investing. It is almost always true that r >= 0, and this is

the case to keep in mind. However, the mathematics we develop requires only

that r > -1.

Kindly guide
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There are situations that result in an effective negative interest rate:

If your time period is fixed, at one year for example, a situation that resulted in costs and/or liabilities much greater than the original investment could be modeled as an arbitrarily large negative interest rate.  Discovering that you have bought a day-care center on a toxic waste dump might be one example.
Perhaps a better statement of the problem would be a good start.  That's rather expected... not here necessarily but in the real world.

if 1+r>0, then r>-1

Is this a given statement?  If so, it's a truism. One follows from the other.

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