Hello readers!!
Welcome to the end of Week 6 of classes and I hope that everyone has done well for the first term test. For me, this was quite the experience, as I've never felt so unsure about my own answers, but we shall see in probably a week or 2's time. I do apologize for not writing over the Thanksgiving break, but I assure you that I will be back on track for the rest of the semester!
Today I'd like to talk about the different ways to prove things. I won't be going into all of them, as some are more self explanatory than others, but I will talk about the ones that I find rather confusing right now, just so I can use this post to help myself sort out some things.
Proof by cases:
When encountering a statement in which you feel that there is more sides to the statement to look at than what you can prove with just one line of thought, then we use proof by cases. We must, of course, think about all the different cases that are possible first, and then we prove each case individually.
Proof by contradiction:
This method of proof is used when you feel that it's probably easier to assume the statement is right (even though you know it's wrong) and to show that it's totally impossible for the proof to work if you keep going down this path!!! It's pretty useful for when your negation statement is difficult to prove or it could be just that the contradiction is easier!
Today's message of the day is to always try to approach a problem several different ways before actually immersing yourself into solving it. It could save you loads of time and effort if you make use of all the tools available to you!
Have a great week everyone!
Lana :)
Welcome to the end of Week 6 of classes and I hope that everyone has done well for the first term test. For me, this was quite the experience, as I've never felt so unsure about my own answers, but we shall see in probably a week or 2's time. I do apologize for not writing over the Thanksgiving break, but I assure you that I will be back on track for the rest of the semester!
Today I'd like to talk about the different ways to prove things. I won't be going into all of them, as some are more self explanatory than others, but I will talk about the ones that I find rather confusing right now, just so I can use this post to help myself sort out some things.
Proof by cases:
When encountering a statement in which you feel that there is more sides to the statement to look at than what you can prove with just one line of thought, then we use proof by cases. We must, of course, think about all the different cases that are possible first, and then we prove each case individually.
Proof by contradiction:
This method of proof is used when you feel that it's probably easier to assume the statement is right (even though you know it's wrong) and to show that it's totally impossible for the proof to work if you keep going down this path!!! It's pretty useful for when your negation statement is difficult to prove or it could be just that the contradiction is easier!
Today's message of the day is to always try to approach a problem several different ways before actually immersing yourself into solving it. It could save you loads of time and effort if you make use of all the tools available to you!
Have a great week everyone!
Lana :)
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