The mathematical mystery of zero (0)

Generally, every and anybody that has even the slightest knowledge of mathematics knows that anything divided by zero is indeterminate, undefined or more technically, tends to infinity. The same way we agree that anything multiplied by zero is zero. There are different proofs, postulations and theories that attempt to buttress this idea, from different mathematical perspectives. The most dominant been that if a number is divided by a given divisor to obtain a certain quotient, then, when that same quotient multiplies the original divisor, we should be able to obtain the original number. In other words, multiplication cancels out division and vice versa. 

There are many such proofs and I have decided not to bother you with the cumbersome details.  Most, if not all available facts and figures are in line with the following

• multiplication by Zero equals Zero 
• division of a non-zero number by Zero is undefined
• division of Zero by Zero is indeterminate 

Note: for better understanding, the terms undefined and indeterminate are explained below:

• If a value is undefined, it means that such value does not exist and as such cannot be obtained
• If a value, say k, is indeterminate, it means that such a value could actually exist, but the value is ambiguous, that is, there could be much more than just one value for k.  

This notwithstanding, one can not help but wonder, "what if?"


After all, Science and Mathematics are technically just a bunch of proven and unproven "what if?s".
Having said this, I thus put forward my theory. I believe that the division of "0" by "0", as a matter of fact, is highly subjective. To be able to effectively obtain a value for dividing zero by another zero, one needs to accurately evaluate the source of the zero itself. This statement might sound somewhat puzzling, but, in reality, it is actually very simple. There are different evaluations and calculations that can yield a zero as an answer. For instance, the following values will all give zeroes as their final answers on calculation.

• Log_x1 = 0, the logarithm of 1 to any base equals zero
• 100 - 100 = 0, simple mathematics

Now, using the above values of zero, we can substitute and prove that division of zero by zero can actually be defined or determined.

Below are some evaluations of divisions of zero by another zero

method 1: using simple arithmetic and the principle of the difference of 2 squares:

Therefore 0/0 = 2

method 2: using the reverse of the principle above:

Therefore, 0/0 = 1/2

method 3:using simple logarithm principles:

The above proves the subjectivity of the division of zero by zero. We can see that for different assumptions of the actual value that yielded zero, we obtained different results (i.e. 2, 1/2 and 1). It is therefore my postulation that by substituting the value of zero as other subjective values, different determinate and defined values can be obtained for it.

Below are evaluations of cases where other numbers are divided by zero:


Generally, the laws of logarithms seem to ascend the laws of the zeros, some of the instances where this can be seen are shown below:


Meanwhile, there have been strange and baffling reports of calculations involving divisions by zero causing mechanical and technical faults to mechanical systems. For instance, On September 21, 1997, a division by zero error on board the USS Yorktown (CG-48) Remote Data Base Manager brought down all the machines on the network, causing the ship's propulsion system to fail. Amazing, right? So, next time you want to try this controversial calculation, make sure you are in a secure location without any heavy machinery.


Please, do  make your contributions, thank you

EFFECTS OF CHANGES IN INFORMATION TECHNOLOGY ON MANAGEMENT AND ORGANIZATIONAL STRUCTURE

Information technology (IT) is basically the application of computers(softwares and hardwares) and telecommunications equipment to store, retrieve, transmit and manipulate data, often in the context of a business or other enterprise. Different forms of changes in information technology will have corresponding impacts on all organizations. There will be a need for new types of managerial, diplomatic, and social skills and a concomitant need for a new type of decision making process that will not be accommodated by existing organizational structures.

Technological change will force changes in basic managerial functions. There will be increased responsibility on management for organization outcomes leading to added emphasis on planning, decision making, control, and coordination. These will often rely on computer-based management science techniques which demand a higher intellectual capability of managers. This will produce strain on managers and other individuals, potentially affecting morale, productivity, and output. IT significantly affects strategic options and creates opportunities and issues that managers need to address in many aspects of their business.

Key impacts of information technology improvement on organization and Management

1.Business strategy

IT creates new opportunities for innovation in products and services. Services which used to be delivered in person can now be delivered over networks. Among the key levers are:

• resequencing: including parallel processing of data-bases
• simultaneity: making information instantly available in several systems
• time extension: offering 24 hour a day; 365 days a year service
• portability: taking service and products closer to the user
• re-usability: using information captured for one purpose (e.g. transactions), and using for other purposes (e.g. customer targeting)

2.Organization Culture
Newer types of IT such as electronic mail and groupware are creating significant changes in the way that information flows around group ware, and between them and their customers and suppliers.

3.Organization Structures
For many years it has been argued that IT will enable larger spans of control and the flattening of group ware. This has at last happened, but due as much to initiatives like BPR (business process re-engineering) and the drive to cut costs.

4.Management Processes
IT is rapidly entering the era where it supports unstructured management processes as well as highly routinised business processes.

5.Work
IT is dramatically changing the nature of professional work. There are few offices where professional do not make use of personal computers, and in many jobs involving extensive information and knowledge based work, the use of the computer is often a core activity.

6.The Workplace
The way in which IT diminishes the effect of distance means that it creates a variety of options for reorganizing the workplace.

Implications for Management

These IT impacts have implications for managers of all organizational functions. Among the most important are:

• Understanding the Changing Context of IT - they are required to adapt quickly to changes. Business managers need to be able to see developments in the context of the wider environment in which their business operates.
• Keeping abreast of Developments - not necessarily about the details of the technologies, but about the business impacts. For instance; managers can be adequately informed by meeting suppliers and business consultants, attending conferences, or receiving customized presentations from independent analysts.
• Integrating IT and Business Planning - the IT strategy should support the business strategy and vice versa. This may need new planning processes, hybrid teams, and an increased incorporation of the levers into business plans.
• Addressing Culture Issues - the dimensions of existing and desired culture need to be understood and how proposed systems will affect them. In particular attention needs to be paid to the organization's information culture.
• Experimenting with new Structures - using IT to remove some of the limitations of hierarchy and to encourage the development of innovative teams, using experts located in different functions and places. Managing dispersed teams is challenging but rewarding.
• Ensuring that new systems are customized change proof - our studies have shown many new systems to be developed around existing customized structures and responsibilities. Since these change very rapidly, new systems should be built with organised customized flexibility and change in mind.
• Developing New Skills - more of tomorrow's managers will need to become hybrid managers, combining the knowledge and skills of general management, their own discipline and IT.
• Using IT as a management tool - initiating personal use of IT into every day work. This should include use of decision support tools, groupware, knowledge management solutions and exploiting the Internet.
• Exploiting Information as a Strategic Asset - using the techniques of Information Resources Management to develop it as a valuable resource for internal use, for adding value to customer activities or services, or for creating saleable products.
• Introducing Knowledge Management and Innovation - going beyond information to developing networks of knowledge experts who evolve the organization's knowledge assets to create extra capabilities and value.
• Reorganizing the Workplace - by introducing flexible working and telework. The business benefits of this in terms of productivity and cost savings are such that there are many personal benefits to be achieved by a successful implementation.