False Proof is one of the concepts in Mathematics. This is a quite interesting area. One of my Mathematics professor started his first class with the following question.
Can you prove 1 = -1?
We all said nope.
Then he went to the blackboard and wrote the following proof.
Version 1:
Amazing. Isn’t? This is called False Proof.
There is one more way to prove 1 = -1.
Version 2 :
Now let us see, how is this possible?
Let us take the first proof (False Proof)
The rule is
generally valid only if at least one of the two numbers x or y is positive, which is not the case here. Alternatively, one can view the square root as a 2-valued function over the complex numbers; in this case both sides of the above equation evaluate to {1, -1}.
How about the second version? Is that true? The answer is false again. Below is the explanation.
The equation a bc = (a b )c, when b and/or c are fractions, is generally valid only when a is positive, which is not the case here, leading to an invalid proof.
This one is a simple cool tip on Firefox.
If you want to view a .com site, then simply type the name and press Ctrl+Enter.
“Ctrl+Enter” will add www. as suffix and .com as prefix. Most of us know this. This works in Internet Explorer also.
What if you want to view a .org or .net websites?
Type the site name and press Ctrl+Shift+Enter for .org websites.
Type the site name and press Shift+Enter for .net websites.
Type the site name and press Ctrl+Enter for .com websites.
Enjoy browsing in Firefox.
Its always looks nice when we send some decorated mails to friends and relatives; especially on happy occastions, b’day wishes etc.
Recently I noticed that Yahoo Mail provides stationery for all yahoo users. (How did not I notice this feature?)
How to get this?
When you compose mail, you will find a button under the Subject field called “Stationery”.
Just click Stationery to get your mail stationeries. This is one of the featuer I always look for, from Yahoo Mail.
The below images will guide you to get this feature.
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There are 46 stationeries available under six different categories. In addition to that, there is a huge list of Solid Colors you can use in your mail.
Are you still using the classic Yahoo interface? Now it is the time to switch to the rich Yahoo Mail interface.
We all know that Google provides shortcuts for most of the actions in GMail and Google Reader.
For example, GMail provide shortcuts like,
- c – Compose
- /- Search
- r – Reply
- f - Forward
These shortcuts can be found here GMail Shortcuts and Google Reader Shortcuts. But while composing some mail, we can’t always visit this link to find a shortcut. I feel that it is difficult.
So what is the easy solution for this? Google gives an easier way to find keyboard shortcuts.
? Key is the solution for this.
Yes, you can get Google Keyboard shortcuts by pressing ? key in your keyboard.
Login to GMail or Google Reader and press ? key in the keyboard. You will get all keyboard shortcuts like below.
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The images given above are taken from GMail and Google Reader.
Simple, isn’t? So, start using ? key to get familiarised with Google Shortcuts.
Do you want to make your emails more stylish? Then decorate your email signature with email icons.
www.services.nexodyne.com is one of the sites where you can generate email icons.
You can use email icons in your websites, blogs, forums. One of the advantages in using icons in public websites is to avoid spam.
Below image is the screenshot from nexodyne.
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Vijay For Victory
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