Is this True for all no.s?

Thread starter johncena
Start date Aug 21, 2009

In summary, when determining if a statement is true for all numbers, it is important to carefully consider the statement and its conditions. It may be possible to provide an example to prove its truth or use mathematical methods such as induction or contradiction. However, there are also many statements that are known to be true for all numbers, such as mathematical principles and laws. To determine if a statement is true for all numbers, logical reasoning and testing with different numbers can be used, but further research may be needed for more complex statements.

Aug 21, 2009

johncena

Is this True for all no.s??

Is this true for all no.s (a)?
a-a = a*0

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Aug 21, 2009

Elucidus

In any number system that has additive and multiplicative identities, additive inverses, and is distributive, yes.

[tex]a \cdot 0 = a \cdot (0+0) = (a \cdot 0) + (a \cdot 0)[/tex]

This can only be true if [itex]a \cdot 0 = 0[/itex]

[tex]a - a = a + (-a) = 0 \text{ by defintion.}[/tex]

--Elucidus

1. Is this statement true for all numbers?

It depends on the statement in question. Some statements may be true for all numbers, while others may only be true for certain numbers or within a certain range. It is important to carefully consider the statement and its conditions before determining if it is true for all numbers.

2. Can you provide an example to prove this statement is true for all numbers?

Yes, if the statement is true for all numbers, then it should be possible to provide an example that demonstrates its truth. However, if the statement is not true for all numbers, then it may not be possible to provide an example that proves it to be true.

3. How do you prove that a statement is true for all numbers?

There are several ways to prove that a statement is true for all numbers. One method is to use mathematical induction, which involves proving that the statement is true for the first few numbers and then showing that if it is true for a specific number, it must also be true for the next number. Another method is to use a proof by contradiction, where you assume the statement is false and then show that this leads to a contradiction, thus proving the statement to be true.

4. Is there a statement that is true for all numbers?

Yes, there are many statements that are true for all numbers. For example, the statement "every number is either even or odd" is true for all numbers. Additionally, mathematical principles and laws such as the commutative property or the distributive property are also true for all numbers.

5. How do you know if a statement is true for all numbers or not?

To determine if a statement is true for all numbers, you can use logical reasoning and mathematical principles to analyze the statement and its conditions. You can also test the statement with different numbers to see if it holds true. However, there may be some statements that are difficult to prove or disprove for all numbers, and in those cases, further research and analysis may be necessary.