Proving Nonnegativity of 3 Numbers with Crazy Exponents | Nonconstructive Proof

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The discussion revolves around proving the nonnegativity of the product of two specific numbers without evaluating them directly. Participants suggest that the proof is likely nonconstructive, as it does not require finding specific values but rather demonstrating a property. One contributor mentions using the law of exponents to analyze the expressions, indicating that if both numbers are negative, their product will be positive. The conversation highlights the challenge of approaching the proof without direct computation. Overall, the focus is on understanding the nature of the proof and the implications of the numbers' relationships.
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Homework Statement


I barely even know where to begin with this proof:

Show that the product of two of the numbers 651000 - 82001 + 3177, 791212 - 92399 + 22001 and 244493 - 58192 + 71777 is nonnegative.

I also have to state if it is constructive or nonconstructive, and I'm not supposed to evaluate the numbers.

Homework Equations


The Attempt at a Solution


The most I can come up with so far is that the proof is likely "nonconstructive" since I am not out to find a single element to make the statement true; I have to determine it in another fashion.
 
Last edited:
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n00neimp0rtnt said:

Homework Statement


I barely even know where to begin with this proof:

Show that the product of two of the numbers 651000 - 82001 + 791212 - 92399 + 2001 and 244493 - 58192 + 71777 is nonnegative.

I also have to state if it is constructive or nonconstructive, and I'm not supposed to evaluate the numbers.


Homework Equations





The Attempt at a Solution


The most I can come up with so far is that the proof is likely "nonconstructive" since I am not out to find a single element to make the statement true; I have to determine it in another fashion.

Well, I have not studied this so please take my suggestion with a grain of salt but: it seems to me that, according to the law of exponents, you can add exponents to arrive at a value (1000-2001+1212-2399 = -187). When you do this, both numbers have a negative value (though we do not know the magnitude), which means the product will have to be positive.
 
Last edited:
I have revised the equation. Can anyone assist me?
 

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